Ans. If a language L is decidable there exists a decider D that decides L. Then
If we run TM D on input ?D? then D accepts ?D? if and only if D doesn't If a language L is of Type DEC
each terminal l ? ? the CFG G0 has a rule S ? lS in R. Also
4.4.1 Consider the following Turing machine Create a DFA B such that L(B) = ?* ... Furthermore M will accept those DFA's whose language is.
If H rejects accept.” 2. Page 3. 4. Consider the emptiness problem for Turing machines: ETM = { ?M?
Accept if T accepts reject if T rejects.” Proof #2: The following TM decides ALLDFA: S = “On input ?A?
Show that if M is a DFA that recognizes language B
Prove that C is Turing-recognizable iff a decidable language D exists such Let T = {?M?
(a) REJECTTM is defined as {?Mw?
then L(M2) is the non-context-.
Let L be the language such that every pair of adjacent 0's appear before A Turing machine M accepts an input w ? ?? if there is a sequence of states.
An example of a DFA in S: A DFA that accepts all strings (b) Ans To show S is decidable we construct a decider D for S as follows (Let C be a TM
Turing-decidable language Answer: A language A that is decided by a Turing machine; i e there is a Turing machine M such that M halts and accepts on any
Consider the decision problem of testing whether a DFA and a regular expression are equivalent Express this problem as a language and show that it is decidable
Construct a Turing machine T to show that S is decidable Let MR be the DFA that accepts the reverse of strings that are accepted by M Then L(MR) = L(M)
Problem 4 3: Let ALLDFA = {?A? A is a DFA that recognizes ?*} Show that ALLDFA is decidable Proof #1: The following TM decides ALLDFA: S = “On input
ADFA is decidable Theorem The language ADFA = {Bw B is a DFA that accepts the string w} is decidable Proof We want to build a TM M that decides ADFA:
Theorem The set of regular languages is closed under the kleene star operation Proof Let L be a regular language We need to show that L
Prove that C is Turing-recognizable iff a decidable language D exists such Let T = {?M?M is a TM that accepts wR whenever it accepts w}(wR is the
nor do they accept any liabilities with respect to the programs S = {a ? D P(a) = TRUE} or simply S if the domain D is obvious from the context