-2
votes
0answers
37 views

Pumping Lemma & Regular Language

For each regular language L, we have an integer k such that: ...
0
votes
1answer
15 views

Algorithm that takes input desc. of two PDAs and outputs intersection of langs. recognized by two PDAs

Does there exist an algorithm which takes as input the descriptions of two pushdown automata, $P1$ and $P2$, and prints the description of another pushdown automaton which recognizes the intersection ...
0
votes
1answer
17 views

Deciding TM which fails to halt whenever the length of its input string is a prime number

I have the following Statement: "A TM called $A$ which fails to halt (i.e runs forever) whenever the length of its input string is a prime number, and eventually halts for all other input strings" ...
-1
votes
1answer
21 views

disproving union of infinitely many regular languages

I want to disprove the following statement: "if $L$ is the union of infinitely many regular languages, then $L$ is guaranteed to be a regular language." I don't know where to start. Any hint will be ...
0
votes
0answers
42 views

predicate logic with assumption NP $\neq$ CO-NP?

Anyone could describe why: Set of All Tautology in propositional logic with assumption NP $\neq$ CO-NP is CO-NP Complete. Thanks. I ask it here before: Is the language of tautologies NP-complete? ...
1
vote
3answers
46 views

Reducing a Decidability Problem to the Halting Problem

Let $L = \{(M, n): M$ halts on less than $n$ elements from a set S $\}$ I'm trying to come up with a generalization on how to solve these types of problems so I have not defined what S is. Since the ...
0
votes
3answers
106 views

What is the difference between regex operations in math and regex in UNIX / Linux?

What is the difference between regular expression operations (union, concatenation, kleene star) and regular expression (implemented in UNIX and can be used together with the grep command)? Are there ...
1
vote
2answers
54 views

Reduction between two languages and a common one

My question is as following : Let $A$ and $B$ be some languages, there exist a language $C$ such that $A\le C$ and $B\le C$, where "$\le$" means "reducible to", so $A\le C$ means there is a mapping ...
1
vote
0answers
89 views

Oracle Turing machine - $E_{\text{TM}}$ and $PCP$.

$$E_{\text{TM}}=\{\langle M\rangle|M\text{ is a TM and $L(M)=\emptyset$}\}.$$ $E_{\text{TM}}$ is undecidable $$PCP=\{\langle P\rangle|P\text{ is an instance of the Post Correspondence Problem with a ...
2
votes
1answer
50 views

Reducing A$_\text{TM}$ to REGULAR$_\text{TM}$

We can solve A$_\text{TM}$ problem using REGULAR$_\text{TM}$. Assume $R$ is a Turing machine that decides REGULAR$_\text{TM}$. We construct $S$ to decide A$_\text{TM}$ as follows On input ...
3
votes
2answers
124 views

context free grammar problem

$L$ is the context free grammar over $\{a, b\}$ $S \rightarrow aSb \; | \;bR \; |\;Ra$ $R \rightarrow bR \;|\;aR\;|\;\epsilon$ Briefly describe this CFG with English sentences and prove your ...
0
votes
2answers
52 views

context free grammar design

Design a context free grammar and PDA for the following language. $$\Sigma = \{0,1\},\qquad L = \left\{uv \mid u \in \sum^{*} \;v\in \sum^{*}1\sum^{*} \text{ with }|u| \geq |v| \right\}$$ I'm not ...
3
votes
2answers
92 views

If $L\in REG$ then $M$ has a finite number of distinct rows

Let $L \subseteq \Sigma^{\star}$ and let $M^{\Sigma^{\star} \times \Sigma^{\star}}(\{0,1\})$ an infinite matrix such that for each $x,y\in \Sigma^\star$: $$ m_{x,y}=\begin{cases} 1 & x y\in L\\ 0 ...
1
vote
1answer
839 views

Language that is recursively enumerable, but not recursive

I have a problem with this task: Show that this language is recursive enumerable, but not recursive: $L = \{ w \in \{0,1\}^* | M_w(x)\; \text{converges for some input}\; x \}$ (where $M$ is turing ...
3
votes
1answer
238 views

Proving Turing Completeness by Simulating Rule 110

Something I've heard often is that Rule 110 is the `simplest' Turing-complete formalism. As a programming exercise in a language I am new to, I implemented a function that computes from an initial ...
7
votes
1answer
208 views

Does there exist a universal pushdown automaton?

Let $\Sigma$ be a fixed alphabet and let $PDA(\Sigma)$ be the set of all Push-Down-Automata (PDA's) having input alphabet $\Sigma$. Is there an alphabet $S$ and a function $f:PDA(\Sigma) \to S^∗$ such ...
2
votes
1answer
141 views

Is the set of codes of Deterministic Finite-State Automata a regular language?

Let $\Sigma$ be a given alphabet. Is there a way to code up Deterministic Finite state Automata (DFA) over $\Sigma$ as strings of $\Sigma$ in such a way that the corresponding subset of $\Sigma^*$ is ...
9
votes
2answers
424 views

Why is it undecidable whether two finite-state transducers are equivalent?

According to the Wikipedia page on finite-state transducers, it is undecidable whether two finite-state transducers are equivalent. I find this result striking, since it is decidable whether two ...
3
votes
3answers
706 views

Is the language of all strings over the alphabet “a,b,c” with the same number of substrings “ab” & “ba” regular?

Is the language of all strings over the alphabet "a,b,c" with the same number of substrings "ab" & "ba" regular? I believe the answer is NO, but it is hard to make a formal demonstration of it, ...