Sipser Problem 3. Notice that this claim follows from Exercise 1. In general, people believe P is a proper subclass of NP In general, it is difficult to find a lower time bound for a given problem NP-completeness Polynomial time reducibility: A <=P B B is NP-complete if B is in NP A <=P B for all A in NP Cook-Levin Theorem: SAT is NP-complete More NP-Complete Problems 3SAT HAMPATH CLIQUE SUBSET-SUM Final Exam. By Theorem 4. Show that ALLDFA is in P. Tariq Malik on December 17, 2016 at 11:59am in CS701 Theory of Computation; Back to CS701 Theory of Computation Discussions. Lecture 32/65: Decidability and Decidable Problems hhp3. CSCI 2670 Introduction to Theory of Computing October 19, 2004 Agenda Last week Variants of Turing machines Definition of algorithm This week Chapter 4 Decidable and - A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. Show that LEN_CFG is decidable. But we only show one here. (c) No, because the input is not in correct form: the second component of the input is missing. Run M 1 on w. Show that ALL DFA is decidable. P is the class of all languages such that if w 2P then there is a deterministic single-tape Turing machine which accepts the string w in polynomial time. ) * (3) All the King’s Horses, and All the King’s Men… Let ALLDFA = { | A is a DFA and L(A) = Σ*} Describe in English what the language ALLDFA consists of. pdf - Free download as PDF File (. 4 Let AεCFG = { G | G is a CFG that generates ε}. Construct a PDA P such that L(P) = fw j w is a palindromeg 2. Consider the decision problem of testing whether a DFA and a regular expression are equivalent. (c) No, because the input is not in correct form: the second component of the input is missing. Express this problem as a language and show that it is decidable. Show that ALLDFA is decidable. Posted by Irfan Khan MSCS on December 18, 2016 at 4:46pm in CS701 - Theory of Computation Mid Term Paper and Final Term Paper; Back to CS701 - Theory of Computation Mid Term Paper and Final Term Paper Discussions. M 1 works as follows. cs701 fall 2016 mid term paper. Homework due next Tuesday (10/26) Slideshow 3839749 by aislin. Show that EQ CFG is undecidable. Use the closure properties of regular languages and context-free languages to show that Lne is not regular 9. txt) or read online for free. There is a single “line valid bit” and three bits, B0, B1,. Let LEN_CFG = { | G is a CFG, k elementof Z^noneg, and L (G) Intersection sigma^k notequalto (where sigma is the alphabet of G)}. Show that for any two languages A and B a language J exists, where A≤T J and B≤T J. 2 Consider the problem of determining whether a DFA and a regular expression are. Sipser Problem 3. Submit to the decider for EQ DFA 3. Last week Variants of Turing machines Definition of algorithm This week Chapter 4 Decidable and undecidable languages The halting problem. Show that ALLDFA is in P. Q#3 Let Alldfa={/A is a DFA and L(A)=∑*}Show that AllDFA is decidable. Show that AεCFG is decidable. show that TRIANGLE Є powered TRIANGLE={IG contains a triangle}. Else, accept. Show that the following language is decidable: SIMPDFA-[A) : A is a DFA with no. FAFASD seeks to spread information, awareness, and hope for families impacted by fetal alcohol spectrum disorder. IScan the input string hG;wi, determining whether the input constitutes a valid CFG. (b) Show that A TM is Turing-recognizable. Let Mbe a Turing machine that decides this language. Create DFA that accept language where number of 0's is even and after every 1 goes 0. Prove that ECFG is a decidable language. Decidable Problems for Context Free Languages Theorem A CFG is decidable, where A CFG = fhG;wijG is a CFG generating wg. Notice that this claim follows from Exercise 1. proof DFA defines same language as minimal DFA. One-to-one function f: T N. •Recall that decidable languages are languages that can be decided by TM (that means, the corresponding TM will accept or reject correctly, never loops) •In this lecture, we investigate some decidable languages that are related to DFA, NFA, and CFG -Testing Acceptance, Emptiness, or Equality •Also, we show how TM can simulate CFG Objectives. List data Prop = Atom String | Not Prop | Imp Prop Prop der. Create a DFA B such that L(B) = Σ * 2. 1 (a) a Yes, because M on input 0100 ends in an accept state. 28) Let Abe a Turing recognizable language consisting of descriptions hMiof Turing machines M that are all deciders. Show that ALLDFA is decidable. Show That The Following. Berkshire Hathaway AGM is still the Warren Buffett show ; US election: Trump’s man in Vegas. It contains 8 KBytes and has a four-way set-associative organization and a block length of four 32-bit words. Does A TM belong to P. Create a DFA B such that L(B) = Σ * 2. Turing-decidable language Answer: A language A that is decided by a Turing machine; i. Let Mbe a Turing machine that decides this language. Show that ALLDFA is in P. Give a PDA that accepts Lpal2 b. Q#3 Let Alldfa={/A is a DFA and L(A)=∑*}Show that AllDFA is decidable. (Hint: Look at the proof for EDFA to get an idea. 2 Consider the problem of determining whether a DFA and a regular expression are. import Data. Show that for any language A , a languages A and B that are Turing-incomparable-that is, where A≤T A. Method II: Suppose on the contrary that L is regular. The sea will have its own, its share of tragedies. Creating DFA to prove closure properties. a Show that P is closed under complement and concatenation. decidable, a decider for A NTM could be to decide A TM. Notice that this claim follows from Exercise 1. (b) Show that A TM is Turing-recognizable. Problem 3 (5 points). Give a CFG that (1) Show "all" DFA is decidable. , Turing machine that halts on all inputs) that decides if two given DFAs accepts the same language. A Prunable State In A DFA Is Some State That Is Never Entered While Processing Any Input String. CS701 - Theory of Computation Mid Term Paper Fall 2016 From 17 December 2016 to 03 January 2017. Construct DFA B that recognizes L(A) ii. 10 Marks (PROBLEM 5. Show that AεCFG is decidable. Given hMi, which represents an automaton M, we can construct an automaton Nsuch that L(N) = L(M)R, that is, Naccepts a word wif and only if Maccepts wR. (Proof idea) IWe construct a Turing machine S to decide the problem. [10 marks] Solution: The following Turing machine decides ALL DFA: M= \on input hBiwhere Bis a DFA: 1. , looping cannot happen. For MSCS, Mega Collection of Solved and Unsolved Past and Current Mid and Final Term Exam Papers, Academic Research Term Papers, Assignments, Guidance, and all about MSCS. Create a DFA B such that L(B) = Σ * 2. Then it accepts if L(D) is empty, otherwise it rejects. Show that ALL DFA is decidable. A and B are DFAs and L(A) C Problem 4 (5 points). Construct a PDA P0 such that L(P0) = L(P)\L(M) 3. A triangle in an undirected graph is a 3-clique. Decidable Problems for Context Free Languages Theorem A CFG is decidable, where A CFG = fhG;wijG is a CFG generating wg. Chapter 3: The Physical Science of the Environment Searching for life elsewhere Looking for life o Probes sent to space o Mars: new focus Viking ½ Evidence of water encouraging because all organisms require water to. Irish: ·sea Proverb: Bainfidh an fharraige a cuid féin amach; beidh a cuid féin ag an bhfarraige. , looping cannot happen. In general, people believe P is a proper subclass of NP In general, it is difficult to find a lower time bound for a given problem NP-completeness Polynomial time reducibility: A <=P B B is NP-complete if B is in NP A <=P B for all A in NP Cook-Levin Theorem: SAT is NP-complete More NP-Complete Problems 3SAT HAMPATH CLIQUE SUBSET-SUM Final Exam. Show that ALLDFA is decidable. Mega Collection of CS701 Mid Term Exam Papers Spring 2015 Dated 04-07-2015 to 09-04-2015 of MSCS of Virtual University of Pakistan (VU) at mscsvu. P is the class of all languages such that if w 2P then there is a deterministic single-tape Turing machine which accepts the string w in polynomial time. 2 Consider the problem of determining whether a DFA and a regular expression are. Show that decidable languages are closed under: (a) union (b) concatenation (c) Kleene star (d) complement (e) intersection Answer: For all of these answers, let L, L1 , and L2 be decidable languages, and M , M1 , and M2 be the TM's that decide them. FAFASD seeks to spread information, awareness, and hope for families impacted by fetal alcohol spectrum disorder. Exercise 4. com - id: 56456d-ZGMxZ. 2) Let INFINITEDFA = { | A is a DFA and L(A) contains an infinite number of strings}. E(dfa) is a decidable language. a Show that P is closed under complement and concatenation. Proof: A DFA accepts some string iff reaching an accept state from the start state by >traveling along the arrows of the DFA is possible. Homework Solution - Set 7 Due: Friday 10/24/08 1. Q#3 Let Alldfa={/A is a DFA and L(A)=∑*}Show that AllDFA is decidable. Prove that ECFG is a decidable language. Answer: The universal TM U recognizes A TM, where U is deﬁned as follows: U = "On input hM,wi, where M is a TM and w is a string: 1. 24 on page 88 in the textbook. CSE 105 Sp04, Problem Set 3 Solutions 3 Want: To show that INFINITEDFA is decidable, meaning to construct a TM M that decides INFINITEDFA. , exhibit a decision procedure for this language): L = {ha,b,ci : a, b and c are regular expressions and a2 ∪b2 = c2. The Intel 80486 has an on-chip,unified cache. DFA is decidable. CSCI670CSCI670IntroductiontoTheoryofIntroductiontoTheoryofComputingComputingComputingComputingOctober13005AgendaAgenda•Yesterday-Decidabilityandregularlanguages. Give a CFG that (1) Show "all" DFA is decidable. Show that ALLDFA is decidable. Since EQ DFA is decidable, we assume that is an algorithm M (i. Answer: Deﬁne the language as C= {hM,Ri | M is a DFA and Ris a regular expression with L(M) = L(R)}. FAFASD seeks to spread information, awareness, and hope for families impacted by fetal alcohol spectrum disorder. Let A(CFG = { | G is a CFG that generates (}. , there is a Turing machine M such that M halts and accepts on any input w ∈ A, and M halts and rejects on input input w ∈ A; i. Else, accept. (a) Show that L is not regular. cs701 fall 2016 mid term paper. Show that ALLDFA is in P. (b) No, because M on input 011 ends in a non-accept state. October 13, 2005. Videos recorded Spring 2014 for CSE355 at Arizona State University. 173 and the fact that each region is no-empty. Answer: Deﬁne the language as C= {hM,Ri | M is a DFA and Ris a regular expression with L(M) = L(R)}. Showing up. Thelanguageweareconcernedwithis INFINITEDFA =fhAi: A isaDFAandL(A)isaninﬂnitelanguageg: Want: To show that INFINITEDFA is decidable, meaning to construct a TM M that decides INFINITEDFA. CSCI 2670 Introduction to Theory of Computing October 13, 2005. 10 Marks (PROBLEM 5. Posted by + M. M 1 works as follows. Show that ALLDFA is decidable. Use K to check if L(G) is empty. Course goals. Express this problem as a language and show that it is decidable. Given a CFG G and a variable A, consider the problem of testing whether A is usable. cs701 fall 2016 mid term paper. Announcements. We show that Sis decidable. Show that, by giving an example, that part (a) is not necessarily true if you replace both A's by A. Decidable Problems for Context Free Languages Theorem A CFG is decidable, where A CFG = fhG;wijG is a CFG generating wg. Show that AεCFG is decidable. Convert P0 into an equivalent CFG G 4. Run M 1 on w. 15 (a) We want to show that if L 1 and L 2 are decidable, then L 1 [L 2 = L 3 is decidable. 2 Consider the problem of determining whether a DFA and a regular expression are. The cache is organized into 128 sets. Let Cbe the DFA obtained by interchanging accepting and rejecting states of B. P is the class of all languages that are decidable by deterministic single-tape Turing machines running in polynomial time. Does A TM belong to P. 5 (EQUIVdfa is decidable), the condition L(A)=L(S) is decidable, and so determining if A belongs to ALLdfa is decidable too. Show that the SPCP is decidable. Irish: ·sea Proverb: Bainfidh an fharraige a cuid féin amach; beidh a cuid féin ag an bhfarraige. Question 2. Express this problem as a language and show that it is decidable. 2 (Decidable Languages) Show that the following languages are decidable: (a) EQ. Given a CFG G and a variable A, consider the problem of testing whether A is usable. Show that INFINITE DFA is decidable. Show that ALLDFA is decidable. Being able to do the job. Let ALLDFA-{(A): A Is A DFA And L(A) = Σ*). It contains 8 KBytes and has a four-way set-associative organization and a block length of four 32-bit words. ThismeansthatforallDFAsA wewant †IfL(A)isaninﬂnitelanguagethenM(hAi)accepts †IfL(A)isaﬂnitelanguagethenM(hAi)rejects. Show that ALLDFA is decidable. Therefore, A NTM cannot be in PSPACE, so A NTM is not PSPACE-complete. We show that Sis decidable. P is the class of all languages such that if w 2P then there is a deterministic single-tape Turing machine which accepts the string w in polynomial time. DFA with an accepting state in the initial state. The cache is organized into 128 sets. Prove that ECFG is a decidable language. Convert P0 into an equivalent CFG G 4. Express this problem as a language and show that it is decidable. Homework due next Tuesday (10/26) Slideshow 3839749 by aislin. Run M1 on w. List data Prop = Atom String | Not Prop | Imp Prop Prop der. Given a CFG G and a variable A, consider the problem of testing whether A is usable. Posted by + M. Exercise 4. Homework 8Solutions. All DFA = {| A is DFA and L(A)= ∑ *} show that is AllDFA decidable (Exercise 4. To test this condition, we can design a >TM T that uses a marking algorithm similar to that used in Example 3. Let SUBSETDFA-A, B L(B)). com - id: 56456d-ZGMxZ. Show that the collection of decidable languages is closed under union. Q#3 Let Alldfa={/A is a DFA and L(A)=∑*}Show that AllDFA is decidable. FAFASD seeks to spread information, awareness, and hope for families impacted by fetal alcohol spectrum disorder. Let Lpal2 be the language wwRvvR:w, v E E' a. If T accepts, “accept”. Show that ALLDFA is reducible to EDFA by constructing a reduction f from ALLDFA to EDFA (in a form of a Turing machine) such that 〈A〉 ∈ ALLDFA ↔ f(〈A〉) ∈ EDFA Expert Answer (Solved) : Write a function that has one input, an integer number n, and one output, an array factors. (a) union: Construct TM M which decides the union of L1 and L2 : On input w: 1. Construct a PDA P such that L(P) = fw j w is a palindromeg 2. Show that ALLDFA is decidable. It will not accept inputs with a 1, but there is no reject state that will cause this DFA to be rejected by the decider. Consider the following algorithm for deciding whether a given non-empty string s of length n belongs to A∗: For ev-ery possible way of splitting s into non-empty substrings s =. import Data. Note: The next question is a programming question. P is the class of all languages that are decidable by deterministic multi-tape Turing machines running in polynomial time. Solution Outline: (a) Method I: Let D i,i ≥ 1 be the DFA that recognizes the language {1i}. A triangle in an undirected graph is a 3-clique. Full text of "Introduction To Theory Of Computation" See other formats. Thelanguageweareconcernedwithis INFINITEDFA =fhAi: A isaDFAandL(A)isaninﬂnitelanguageg: Want: To show that INFINITEDFA is decidable, meaning to construct a TM M that decides INFINITEDFA. Question 2. Let L 1 and L 2 be decidable languages, and M 1 and M 2 be the Turing machines that decide them. Method II: Suppose on the contrary that L is regular. CSE 105 Sp04, Problem Set 3 Solutions 3 Want: To show that INFINITEDFA is decidable, meaning to construct a TM M that decides INFINITEDFA. Create a DFA B such that L(B) = Σ * 2. If M accepts w, accept; if M rejects w, reject. Show thatALLDFAis decidable. (In each transition, we can read the top of both stacks and push something on top of both stacks, if we choose. Use the closure properties of regular languages and context-free languages to show that Lne is not regular 9. Idea: If G is in CNF, then it takes at most 2n 1 steps to generate w. Yesterday Decidability and regular languages Today Putting things in perspective More on decidability and regular languages Decidability and context free grammars. Problem 3 (5 points). 24 on page 88 in the textbook. CSCI 2670 Introduction to Theory of Computing. (Proof idea) IWe construct a Turing machine S to decide the problem. A “good old boy” who can get along with others. Show That The Following. (c) No, because the input is not in correct form: the second component of the input is missing. The cache is organized into 128 sets. Construct a PDA P0 such that L(P0) = L(P)\L(M) 3. Homework Solution - Set 7 Due: Friday 10/24/08 1. Loading Autoplay When autoplay is enabled,. Turing-recognizable language. Show that ALL NFA = fhMi: L(M) for the NFA Mwhose input alphabet is gis in PSPACE. DFA with an accepting state in the initial state. CSCI 2670 Introduction to Theory of Computing October 13, 2005. All DFA = {| A is DFA and L(A)= ∑ *} show that is AllDFA decidable (Exercise 4. pdf), Text File (. Show that NP is closed under union and concatenation. Show that ALL DFA = fhBijBgis DFA and L(B) = gis decidable. 1 Answer to Let ALL DFA = {hAi| A is a DFA and L(A) = Σ∗ }. Show that ETM, the complement of. 3) Answer: Consider the following Turing machine M = " on input , where A is a DFA 1. 3) Answer: Consider the following Turing machine M = “ on input , where A is a DFA 1. A And B Are DFAs And L(A) C Problem 4 (5 Points). Notice that this claim follows from Exercise 1. Use the closure properties of regular languages and context-free languages to show that Lne is not regular 9. txt) or read online for free. decidable, a decider for A NTM could be to decide A TM. The cache is organized into 128 sets. 3 Let ALLDFA = { | A is a DFA that recognizes (*}. CSE 105 Sp04, Problem Set 3 Solutions 3 Want: To show that INFINITEDFA is decidable, meaning to construct a TM M that decides INFINITEDFA. Show that ALLDFA is decidable. Let Cbe the DFA obtained by interchanging accepting and rejecting states of B. The sea will have its own, its share of tragedies. Problem 1 For this problem you may assume the containment diagram in Figure 4. Show that the set of incompressible strings is un decidable. ) * (3) All the King's Horses, and All the King's Men… Let ALLDFA = { | A is a DFA and L(A) = Σ*} Describe in English what the language ALLDFA consists of. List data Prop = Atom String | Not Prop | Imp Prop Prop der. Various application areas, such as modern cryptographic protocols, rely on theoretical principles that you will learn here. Able to give care, to show care, to just care. 3 Let ALLDFA = { | A is a DFA that recognizes (*}. Let build M0as follows: M0= \On input w: 1. , looping cannot happen. Given a CFG G and a variable A, consider the problem of testing whether A is usable. It will not accept inputs with a 1, but there is no reject state that will cause this DFA to be rejected by the decider. Run M 1 on w. 3 Let ALLDFA ={ (A) I A is a DFA and L(A) = Sigma* }. decidable, a decider for A NTM could be to decide A TM. CSCI 2670 Introduction to Theory of Computing. Show that ALLDFA is in P. pdf using cvssubmit. Let T = “On input where A is a DFA i. To show PALDFA is decidable, we construct a decider D for PALDFA as follows (Let K be a TM that decides ECFG): D = \On input hMi, 1. Then it accepts if L(D) is empty, otherwise it rejects. (b) No, because M on input 011 ends in a non-accept state. Clearly, hMi2Sif and only if L(M) = L(N). Show That LEN_CFG Is Decidable. (a) Show that L is not regular. Homework Solution - Set 7 Due: Friday 10/24/08 1. If T rejects, “reject” 2. Let CONNECTED={IG is a connected undirected graph}. Show that, by giving an example, that part (a) is not necessarily true if you replace both A's by A. Show that ALL DFA is decidable. The Intel 80486 has an on-chip,unified cache. Show That ALLDFA Is Decidable. (a) Show that L is not regular. Let SUBSETDFA-A, B L(B)). Marcela Reyna - Free download as PDF File (. To show PALDFA is decidable, we construct a decider D for PALDFA as follows (Let K be a TM that decides ECFG): D = \On input hMi, 1. Show thatALLDFAis decidable. show that TRIANGLE Є powered TRIANGLE={IG contains a triangle}. Loading Unsubscribe from hhp3? Show more Show less. What to turn in Save your work in the hw10 folder and turn in the files hw10. Show that ALLDFA is decidable. Show that NP is closed under union and concatenation. Let Cbe the DFA obtained by interchanging accepting and rejecting states of B. Yesterday Decidability and regular languages Today Putting things in perspective More on decidability and regular languages Decidability and context free grammars. Show that EQ CFG is undecidable. Use the closure properties of regular languages and context-free languages to show that Lne is not regular 9. Homework Solution - Set 7 Due: Friday 10/24/08 1. In general, people believe P is a proper subclass of NP In general, it is difficult to find a lower time bound for a given problem NP-completeness Polynomial time reducibility: A <=P B B is NP-complete if B is in NP A <=P B for all A in NP Cook-Levin Theorem: SAT is NP-complete More NP-Complete Problems 3SAT HAMPATH CLIQUE SUBSET-SUM Final Exam. 17 December cs701 paper CS701 Q#1suppose there is a language L we know that L is Turing. Consider the decision problem of testing whether a DFA and a regular expression are equivalent. Show that A is decidable. Homework Solution - Set 7 Due: Friday 10/24/08 1. Exercise 4. Express this problem as a language and show that it is decidable. import Data. Show that ALL DFA is decidable. If L(G) is empty, reject. show that TRIANGLE Є powered TRIANGLE={IG contains a triangle}. ThismeansthatforallDFAsA wewant †IfL(A)isaninﬂnitelanguagethenM(hAi)accepts †IfL(A)isaﬂnitelanguagethenM(hAi)rejects. DFA RE = fhD;Ri j Dis a DFA and Ris a regular expression and L(D) = L(R)g Solution: We know from the lecture that EQ. Show that the SPCP is decidable. Theory also is relevant to you because it shows you a new, simpler, and more elegant side of computers, which we normally consider to be complicated machines. CS701 - Current Mid Term Papers Dated: 04-07-2015. Loading Unsubscribe from hhp3? Show more Show less. Show that SUBSETDFA is decidable. pdf), Text File (. To test this condition, we can design a >TM T that uses a marking algorithm similar to that used in Example 3. 3 Let ALLDFA = { A | A is a DFA and L(A) = Σ∗}. Show that NP is closed under union and concatenation. Show that ALLDFA is reducible to EDFA by constructing a reduction f from ALLDFA to EDFA (in a form of a Turing machine) such that 〈A〉 ∈ ALLDFA ↔ f(〈A〉) ∈ EDFA Expert Answer (Solved) : Write a function that has one input, an integer number n, and one output, an array factors. Show that the collection of decidable languages is closed under union. Give a PDA that accepts Lpal2 b. Lecture 32/65: Decidability and Decidable Problems hhp3. A language L belongs to P iff L 2TIME(2n). Show that SUB DFA is decidable, i. To show PALDFA is decidable, we construct a decider D for PALDFA as follows (Let K be a TM that decides ECFG): D = \On input hMi, 1. Homework 8Solutions. Turing-recognizable language. ThismeansthatforallDFAsA wewant †IfL(A)isaninﬂnitelanguagethenM(hAi)accepts †IfL(A)isaﬂnitelanguagethenM(hAi)rejects. Show that NP is closed under union and concatenation. Homework 8Solutions 1. We construct a. Department of Computer Science COMPSCI 350 Assignment 2 Due: May 15 1. A triangle in an undirected graph is a 3-clique. Show that decidable languages are closed under: (a) union (b) concatenation (c) Kleene star (d) complement (e) intersection Answer: For all of these answers, let L, L1 , and L2 be decidable languages, and M , M1 , and M2 be the TM's that decide them. Give a CFG that (1) Show "all" DFA is decidable. Answer: Deﬁne the language as C= {hM,Ri | M is a DFA and Ris a regular expression with L(M) = L(R)}. 3 Let ALLDFA ={ (A) I A is a DFA and L(A) = Sigma* }. The following DFA (with an alphabet of 0 and 1) is an example of this. A Scottish start-up that is bidding to send satellites into orbit from the UK with a reusable rocket launcher is aiming to raise €5m through a listing on Malta’s new junior market. The cache is organized into 128 sets. A prunable state in a DFA is some state that is never entered while processing any input string. 2 (Decidable Languages) Show that the following languages are decidable: (a) EQ. Convert P0 into an equivalent CFG G 4. A Scottish start-up that is bidding to send satellites into orbit from the UK with a reusable rocket launcher is aiming to raise €5m through a listing on Malta’s new junior market. Let ALLDFA = { | A is a DFA and L(A) = Σ* }. We show that EQ CFG is undecidable by showing that if it would be decidable, then so would ALL CFG, which is not true (Theorem 5. Keeping your cool. The cache is organized into 128 sets. A language L belongs to P iff there is a constant k and a decider M running in time O(nk) such that L = L(M). Let SUB_DFA = { | A, B Are DFAs, And L(A) L(B)}. If M accepts w, accept; if M rejects w, reject. Let LEN_CFG = { | G is a CFG, k elementof Z^noneg, and L (G) Intersection sigma^k notequalto (where sigma is the alphabet of G)}. Turing-recognizable language. a Show that P is closed under complement and concatenation. Let LEN_CFG = { | G Is A CFG, K Elementof Z^noneg, And L(G) Intersection Sigma^k Notequalto (where Sigma Is The Alphabet Of G)}. Show that SUB DFA is decidable, i. 10 Marks (PROBLEM 5. (b) No, because M on input 011 ends in a non-accept state. Show that, if A is nonempty, A contains some string of length at most k. Turing-decidable language Answer: A language A that is decided by a Turing machine; i. Since EQ DFA is decidable, we assume that is an algorithm M (i. Show that ETM, the complement of. Showing up. Chapter 3: The Physical Science of the Environment Searching for life elsewhere Looking for life o Probes sent to space o Mars: new focus Viking ½ Evidence of water encouraging because all organisms require water to. All DFA = {| A is DFA and L(A)= ∑ *} show that is AllDFA decidable (Exercise 4. Consider the following algorithm for deciding whether a given non-empty string s of length n belongs to A∗: For ev-ery possible way of splitting s into non-empty substrings s =. Show that SUB DFA is decidable, i. P is the class of all languages that are decidable by deterministic multi-tape Turing machines running in polynomial time. Show that SUBSETDFA is decidable. (a) Show that L is not regular. Yesterday Decidability and regular languages Today Putting things in perspective More on decidability and regular languages Decidability and context free grammars. Decidable Problems for Context Free Languages Theorem A CFG is decidable, where A CFG = fhG;wijG is a CFG generating wg. Solution Outline: (a) Method I: Let D i,i ≥ 1 be the DFA that recognizes the language {1i}. tex and hw10. To show PALDFA is decidable, we construct a decider D for PALDFA as follows (Let K be a TM that decides ECFG): D = \On input hMi, 1. (Hint: Look at the proof for EDFA to get an idea. Show that EQ CFG is undecidable. Hint: In this case, all the states that are reachable from the start state are final states. (b) Show that L is decidable. Berkshire Hathaway AGM is still the Warren Buffett show ; US election: Trump’s man in Vegas. (Families Affected by Fetal Alcohol Spectrum Disorder). Show thatALLDFAis decidable. Prove that ECFG is a decidable language. A “good old boy” who can get along with others. From input hB;Cia Turing machine constructs a DFA Drecognizing L(B)\L(C). CSE 105 Sp04, Problem Set 3 Solutions 3 Want: To show that INFINITEDFA is decidable, meaning to construct a TM M that decides INFINITEDFA. pdf - Free download as PDF File (. ) * (3) All the King's Horses, and All the King's Men… Let ALLDFA = { | A is a DFA and L(A) = Σ*} Describe in English what the language ALLDFA consists of. 2 (Decidable Languages) Show that the following languages are decidable: (a) EQ DFA RE = fhD;Ri j Dis a DFA and Ris a regular expression and L(D) = L(R)g Solution: We know from the lecture that EQ DFA = fhA;Bi j Aand Bare DFAs and L(A) = L(B)g is decidable. October 19, 2004. CSCI 2670 Introduction to Theory of Computing. Therefore, A NTM cannot be in PSPACE, so A NTM is not PSPACE-complete. If T accepts, “accept”. Show that ALLDFA is in P. There is a single "line valid bit" and three bits, B0, B1,. Show that ALL DFA = fhBijBgis DFA and L(B) = gis decidable. tex and hw10. M 1 works as follows. Show a Turing Machine accepts all DFAs. CS701 - Current Mid Term Papers Dated: 04-07-2015. proof DFA defines same language as minimal DFA. All DFA = {| A is DFA and L(A)= ∑ *} show that is AllDFA decidable (Exercise 4. •Recall that decidable languages are languages that can be decided by TM (that means, the corresponding TM will accept or reject correctly, never loops) •In this lecture, we investigate some decidable languages that are related to DFA, NFA, and CFG –Testing Acceptance, Emptiness, or Equality •Also, we show how TM can simulate CFG Objectives. Then, {(hD ii, )} i≥1 constitutes an inﬁnite collection of distinguishable strings. Thelanguageweareconcernedwithis INFINITEDFA =fhAi: A isaDFAandL(A)isaninﬂnitelanguageg: Want: To show that INFINITEDFA is decidable, meaning to construct a TM M that decides INFINITEDFA. Create a DFA B such that L(B) = Σ * 2. 15 of Sipser book) Q16. A Prunable State In A DFA Is Some State That Is Never Entered While Processing Any Input String. Show thatALLDFAis decidable. 3) Answer: Consider the following Turing machine M = " on input , where A is a DFA 1. A Scottish start-up that is bidding to send satellites into orbit from the UK with a reusable rocket launcher is aiming to raise €5m through a listing on Malta’s new junior market. Show that T is countable. Show that NP is closed under union and concatenation. · billow, swell. Announcements. P is the class of all languages that are decidable by deterministic single-tape Turing machines running in polynomial time. All DFA = {| A is DFA and L(A)= ∑ *} show that is AllDFA decidable (Exercise 4. Show that Th(N,)is decidable. Let CONNECTED={IG is a connected undirected graph}. Q#4 Let LALL ={/M is a TM with i/p ∑ and L(M =∑*} Prove that LALL is not a co Turing recognizable. Show that the following language is decidable: SIMPDFA-[A) : A is a DFA with no. show that TRIANGLE Є powered TRIANGLE={IG contains a triangle}. equivalent. It contains 8 KBytes and has a four-way set-associative organization and a block length of four 32-bit words. Show that the following language is decidable: SIMPDFA-[A) : A is a DFA with no. But we only show one here. Let CONNECTED={IG is a connected undirected graph}. Then, let M be a DFA that. a Show that P is closed under complement and concatenation. Think back to what you learned about NP-completeness. The cache is organized into 128 sets. 28) Let Abe a Turing recognizable language consisting of descriptions hMiof Turing machines M that are all deciders. Run M 1 on w. Keeping a good spirit, one of optimism and openness. (b) No, because M on input 011 ends in a non-accept state. Show that ALLDFA is in P. A and B are DFAs and L(A) C Problem 4 (5 points). Let SUB_DFA = { | A, B Are DFAs, And L(A) L(B)}. Then, {(hD ii, )} i≥1 constitutes an inﬁnite collection of distinguishable strings. October 13, 2005. Show that ALLDFA is decidable. Show that A is decidable. Chapter 3: The Physical Science of the Environment Searching for life elsewhere Looking for life o Probes sent to space o Mars: new focus Viking ½ Evidence of water encouraging because all organisms require water to. The sea will have its own, its share of tragedies. We show that EQ CFG is undecidable by showing that if it would be decidable, then so would ALL CFG, which is not true (Theorem 5. Show that, by giving an example, that part (a) is not necessarily true if you replace both A's by A. The cache is organized into 128 sets. CS701 - Current Mid Term Papers Dated: 04-07-2015. Show thatALLDFAis decidable. Show that AεCFG is decidable. But we only show one here. 17 December cs701 paper CS701 Q#1suppose there is a language L we know that L is Turing. Show that the collection of decidable languages is closed under union. Problem 1 For this problem you may assume the containment diagram in Figure 4. [10 marks] Solution: The following Turing machine decides ALL DFA: M= \on input hBiwhere Bis a DFA: 1. Course goals. Hint: In this case, all the states that are reachable from the start state are final states. Being there. To test this condition, we can design a >TM T that uses a marking algorithm similar to that used in Example 3. Loading Autoplay When autoplay is enabled,. Show that EQ CFG is undecidable. DFA RE = fhD;Ri j Dis a DFA and Ris a regular expression and L(D) = L(R)g Solution: We know from the lecture that EQ. Let Lpal2 be the language wwRvvR:w, v E E' a. It contains 8 KBytes and has a four-way set-associative organization and a block length of four 32-bit words. show that TRIANGLE Є powered TRIANGLE={IG contains a triangle}. " Note that U only recognizes A TM and does not decide A TM Because when we run M on w,. Notice that this claim follows from Exercise 1. pdf using cvssubmit. CS701 ALL Current Mid Term Papers Fall 2016 And Past Mid Term Papers at One Place from 17 December 2016 to 29 December 2016. The cache is organized into 128 sets. Show thatALLDFAis decidable. Show That The Following. , Turing machine that halts on all inputs) that decides if two given DFAs accepts the same language. Create DFA that accept language where number of 0's is even and after every 1 goes 0. Lecture 32/65: Decidability and Decidable Problems hhp3. Method II: Suppose on the contrary that L is regular. Express this problem as a language and show that it is decidable. 1 (a) a Yes, because M on input 0100 ends in an accept state. pdf using cvssubmit. Berkshire Hathaway AGM is still the Warren Buffett show ; US election: Trump’s man in Vegas. Let L 1 and L 2 be decidable languages, and M 1 and M 2 be the Turing machines that decide them. (Hint: Look at the proof for EDFA to get an idea. Creating DFA to prove closure properties. Gaining skills and applying them well. equivalent. Else, accept. Show that ALLDFA is in P. Theory also is relevant to you because it shows you a new, simpler, and more elegant side of computers, which we normally consider to be complicated machines. Show that for any two languages A and B a language J exists, where A≤T J and B≤T J. Chapter 3: The Physical Science of the Environment Searching for life elsewhere Looking for life o Probes sent to space o Mars: new focus Viking ½ Evidence of water encouraging because all organisms require water to. Consider the decision problem of testing whether a DFA and a regular expression are equivalent. Prove that ECFG is a decidable language. Run M on w. Let LEN_CFG = { | G is a CFG, k elementof Z^noneg, and L (G) Intersection sigma^k notequalto (where sigma is the alphabet of G)}. This decider will accept a DFA that does not accept all inputs if, for example, there is no transition for one of the characters in σ. Decidable Problems for Context Free Languages Theorem A CFG is decidable, where A CFG = fhG;wijG is a CFG generating wg. 3) Answer: Consider the following Turing machine M = “ on input , where A is a DFA 1. E(dfa) is a decidable language. Show that ALLDFA is decidable. In general, people believe P is a proper subclass of NP In general, it is difficult to find a lower time bound for a given problem NP-completeness Polynomial time reducibility: A <=P B B is NP-complete if B is in NP A <=P B for all A in NP Cook-Levin Theorem: SAT is NP-complete More NP-Complete Problems 3SAT HAMPATH CLIQUE SUBSET-SUM Final Exam. Show that ALLDFA is in P. Show that INFINITE DFA is decidable. The Intel 80486 has an on-chip,unified cache. 15 (a) We want to show that if L 1 and L 2 are decidable, then L 1 [L 2 = L 3 is decidable. The cache is organized into 128 sets. We show that Sis decidable. Theory also is relevant to you because it shows you a new, simpler, and more elegant side of computers, which we normally consider to be complicated machines. Show that A(CFG is decidable. Method II: Suppose on the contrary that L is regular. List data Prop = Atom String | Not Prop | Imp Prop Prop der. Answer: The universal TM U recognizes A TM, where U is deﬁned as follows: U = "On input hM,wi, where M is a TM and w is a string: 1. give the pseudocode for function def deciderSUB DFA (G) and discussion of correctness. Use K to check if L(G) is empty. Show that ALLDFA is in P. 4 Let AεCFG = { G | G is a CFG that generates ε}. Give a PDA that accepts Lpal2 b. Show That ALL_DFA Is Decidable. (c) No, because the input is not in correct form: the second component of the input is missing. Idea: If G is in CNF, then it takes at most 2n 1 steps to generate w. Show that EQ CFG is undecidable. 3) Let a 2-PDA be a pushdown automata with access to 2 stacks. pdf using cvssubmit. Show that the following language is decidable (ie. A Prunable State In A DFA Is Some State That Is Never Entered While Processing Any Input String. In general, people believe P is a proper subclass of NP In general, it is difficult to find a lower time bound for a given problem NP-completeness Polynomial time reducibility: A <=P B B is NP-complete if B is in NP A <=P B for all A in NP Cook-Levin Theorem: SAT is NP-complete More NP-Complete Problems 3SAT HAMPATH CLIQUE SUBSET-SUM Final Exam. Consider the following algorithm for deciding whether a given non-empty string s of length n belongs to A∗: For ev-ery possible way of splitting s into non-empty substrings s =. Exercise 4. Show that SUBSETDFA is decidable. Run M on w. Show that INFINITEDFA is decidable. A and B are DFAs and L(A) C Problem 4 (5 points). FAFASD seeks to spread information, awareness, and hope for families impacted by fetal alcohol spectrum disorder. txt) or read online for free. [10 marks] Solution: The following Turing machine decides ALL DFA: M= \on input hBiwhere Bis a DFA: 1. Method II: Suppose on the contrary that L is regular. In general, people believe P is a proper subclass of NP In general, it is difficult to find a lower time bound for a given problem NP-completeness Polynomial time reducibility: A <=P B B is NP-complete if B is in NP A <=P B for all A in NP Cook-Levin Theorem: SAT is NP-complete More NP-Complete Problems 3SAT HAMPATH CLIQUE SUBSET-SUM Final Exam. 64 Let N be an NFA with k states that recognizes some language A. Q#3 Let Alldfa={/A is a DFA and L(A)=∑*}Show that AllDFA is decidable. CSE 105 Sp04, Problem Set 3 Solutions 3 Want: To show that INFINITEDFA is decidable, meaning to construct a TM M that decides INFINITEDFA. b Let A be a decidable language and let D be a polytime decider for it. Show that, if A is nonempty, A contains some string of length at most 2k d. Various application areas, such as modern cryptographic protocols, rely on theoretical principles that you will learn here. Construct a PDA P0 such that L(P0) = L(P)\L(M) 3. 2 (Decidable Languages) Show that the following languages are decidable: (a) EQ DFA RE = fhD;Ri j Dis a DFA and Ris a regular expression and L(D) = L(R)g Solution: We know from the lecture that EQ DFA = fhA;Bi j Aand Bare DFAs and L(A) = L(B)g is decidable. The cache is organized into 128 sets. (Proof idea) IWe construct a Turing machine S to decide the problem. Last week Variants of Turing machines Definition of algorithm This week Chapter 4 Decidable and undecidable languages The halting problem. A triangle in an undirected graph is a 3-clique. Idea: If G is in CNF, then it takes at most 2n 1 steps to generate w. Posted by Irfan Khan MSCS on December 18, 2016 at 4:46pm in CS701 - Theory of Computation Mid Term Paper and Final Term Paper; Back to CS701 - Theory of Computation Mid Term Paper and Final Term Paper Discussions. Decidable Problems for Context Free Languages Theorem A CFG is decidable, where A CFG = fhG;wijG is a CFG generating wg. Homework due next Tuesday (10/26) Slideshow 3839749 by aislin. 173 and the fact that each region is no-empty. 1 Answer to Let ALL DFA = {hAi| A is a DFA and L(A) = Σ∗ }. (b) Show that L is decidable. (In each transition, we can read the top of both stacks and push something on top of both stacks, if we choose. 64 Let N be an NFA with k states that recognizes some language A. Then, {(hD ii, )} i≥1 constitutes an inﬁnite collection of distinguishable strings. Notice that this claim follows from Exercise 1. Run M 1 on w. 3) Answer: Consider the following Turing machine M = “ on input , where A is a DFA 1. Let Mbe a Turing machine that decides this language. Homework Solution - Set 7 Due: Friday 10/24/08 1. Show that the following language is decidable (ie. Problem 2 - Semi-Decidability (25 points) Show that the acceptance problem for Turing machines. Posted by + M. FAFASD seeks to spread information, awareness, and hope for families impacted by fetal alcohol spectrum disorder. List data Prop = Atom String | Not Prop | Imp Prop Prop der. CSCI670CSCI670IntroductiontoTheoryofIntroductiontoTheoryofComputingComputingComputingComputingOctober13005AgendaAgenda•Yesterday-Decidabilityandregularlanguages. Last week Variants of Turing machines Definition of algorithm This week Chapter 4 Decidable and undecidable languages The halting problem. Using the procedure given in class, convert the regular expression. Show that LEN_CFG is decidable. 3) Consider counting the ordered pairs of integers in the Cartesian plane. Sipser provides an algorithm for ALL NFA that runs in nondeterministic space O(n), so ALL. Show a Turing Machine accepts all DFAs. Answer: The universal TM U recognizes A TM, where U is deﬁned as follows: U = "On input hM,wi, where M is a TM and w is a string: 1.

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