6. Show that there exists an algorithm to determine whether L = ?* for any regular...
a.) Exhibit an algorithm that, given any three regular languages, L,L1,L2, determines whether or not L = L1L2. b.) Describe an algorithm by which one can decide whether two regular expressions are equivalent.
Show that there exists a non-regular language that satisfies the pumping lemma. In particular, you can consider the following language. nan . You need to show that (1) L is not regular, and (2) L satisfies the pumping lemma.
Show that there exists a non-regular language that satisfies the pumping lemma. In particular, you can consider the following language. nan . You need to show that (1) L is not regular, and (2) L satisfies the pumping lemma.
(d) Let L be any regular language. Use the Pumping Lemma to show that In > 1 such that for all w E L such that|> n, there is another string ve L such that lvl <n. (4 marks) (e) Let L be a regular language over {0,1}. Show how we can use the previous result to show that in order to determine whether or not L is empty, we need only test at most 2" – 1 strings. (2...
6. Determine whether or not the following languages on Σ-(a) are regular (a) L = {an : n > 2, is a prime number) (b) L fa"n : n is not a prime number. (c) L-(an . Ti--k3 for some k 20} Tt . L={an : n = 2k for some k > 0} (e) L an: n is the product of two prime numbers). (f) L = {an : n is either prime or the product of two or...
The grammartofsm algorithm:
Let L be the language described by the following regular grammar: a. For each of the following strings, indicate whether it is a member of L: v. zyyzz b. Use grammartofsm (Rich 2008; page 157) to construct an FSM that accepts L c. Give a concise (but complete) description of L in plain English. We were unable to transcribe this image
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular language L, there exists a pumping length p such that, if s€Lwith s 2 p, then we can write s xyz with (i) xy'z E L for each i 2 0, (ii) ly > 0, and (iii) kyl Sp. Prove that A ={a3"b"c?" | n 2 0 } is not a regular language. S=
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular...
3. Show that there exists a polynomial time algorithm for deciding whether a 2-CNF formula is satisfiable. Hint Note that any clause containing exactly two variables can be written in terms of a conditional, i.e.: Next, look at the directed graph whose nodes are variables (and their negations), and think what happens if there is some cycle containing a variable r and its negation .
Question 1: Every language is regular T/F Question 2: There exists a DFA that has only one final state T/F Question 3: Let M be a DFA, and define flip(M) as the DFA which is identical to M except you flip that final state. Then for every M, the language L(M)^c (complement) = L( flip (M)). T/F Question 4: Let G be a right linear grammar, and reverse(G)=reverse of G, i.e. if G has a rule A -> w B...
-. If L and L2 are regular languages, show the the language BothOr Neither is also regular. Both Or Neither is the language that contains strings that are in both L1 and L, or in neither L or L2.
2. Prove that {a"6"c" |m,n0}is not a regular language. Answer: 3. Let L = { M M is a Turing machine and L(M) is empty), where L(M) is the language accepted by M. Prove L is undecidable by finding a reduction from Aty to it, where Arm {<M.w>M is a Turing machine and M accepts Answer: 4. a) Define the concept of NP-completeness b) If A is NP-complete, and A has a polynomial time algorithm, then a polynomial time algorithm...