Automata Theory, including abstract machines, grammars, parsing, grammatical inference, transducers, and finite-state techniques

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50 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? ...
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62 views

This proof in my textbook involving the pumping lemma appears incorrect - is it?

It states Let $B$ be the language $\{0^n1^n2^n | n \geq 0\}$. We use the pumping lemma to prove that $B$ is not regular. The proof is by contradiction. Assume to the contrary that $B$ is regular. ...
3
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1k views

My Moore and Mealy machines look the same. Why?

For university I have to construct equivalent Mealy and Moore machines that solve certain problems. But I am confused, as my Moore and Mealy machines turn out to have exactly the same nodes, just with ...
2
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27 views

Size of automata or regular expressions avoiding cross patterns

Let $\Sigma$ be an alphabet of finite size $k$, and $n$ some integer. I am interested in the language of words of size $n$ that do not contain $abab$ as a subword, for any pair $(a,b) \in \Sigma$ (I ...
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66 views

Determine the language that corresponds to the following automata.

I want to determine that language that corresponds to the following automata Note: $q_{6}$ have arrow to $a$ to himself. I started with the minimal words: $aaabb$ $aaba$ $aaaba$ $bababa$ the ...
2
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42 views

halting problem

Prove that it is undecidable for the halting problem of a deterministic Turing machine which accepts nonrecursive language or in-other-words: let's say we have a deterministic Turing machine which ...
2
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66 views

Blanks in the Tape of a Turing Machine

I used to have a lot of trouble with Turing Machines, primarily because I thought that in-between input symbols on the tape, one could have an arbitrary number of blanks, so every input would need to ...
2
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28 views

Is there a 2D 3-colorstate mobile automaton that grows like $ln^{0,5}(t)$?

Define an integer function $f(t)$ for an integer $t>25$ such that $|f(f(t)) - ln(t)| < \sqrt {ln(t)}+2$. Define $L(X(t))$ as the number of nonwhite states at iteration $t$ of mobile automaton ...
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51 views

Expressiveness of finite memory programs

Assume we have a simple programming language with while, if, := (assignment), ...
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49 views

Quality of Reduction of finite automata

I am looking for an example, which corresponds to what I've learned in my Applied Automata Theory Class: Given a NFA $\mathcal{A}$, a $\approx _\mathcal{A}$ quotient automaton can be bigger then a ...
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16 views

Help with proving a language is regular (Sipser problem 1.49a)

I am working through Sipser's Introduction to the theory of computation on my own, so I don't have access to a teacher. Hopefully you can help me! Giving hints is highly appreciated. This question is ...
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45 views

Pumping Lemma for Context Free Languages: Is this language CFL?

I am learning for the first time the Pumping Lemma for CFL, and I thought I understood how it works until I came across this example: "Show that $L = \{a^m b^m c^n \mid m \leq n\}$ is not a CFL." My ...
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15 views

how to create transition system/automata for modulo 4

I don't know how to think when to build a transition system/automata to calculate modulo 4 a of binary numbers. I know that the last two binary digits gives the rest but I need to go through hole ...
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33 views

Is this correct way to prove that { $uv$ $\mid$ $u$ and $v$ are strings over $(0,1)$ & $|u| = |v|$ } language is not regular?

I proved this using Pumping Lemma in the following way, Taking $p$ as pumping length then let us take a string $S$ where, $|u| = |v| = p$ Now according to pumping lemma $S$ can be split into three ...
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40 views

Difference between a*b and a*+b? Does the “+” denote Kleene plus or “or”?

Me and a friend are study for a quiz and are trying to determine the difference between the two NFA's produce by the regular exressions a*b and ...
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26 views

Lattice worms with nontrivial deaths

In Paterson's worms, a triangular lattice is used. A worm can move in 6 directions. As each node is hit, the worm follows an internal rule for which edge it will eat next based on the edges already ...
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36 views

Language of Specific Grammar

I ran into this exercise in Sipser's Note on Computation Theory. Consider the following grammar $G$: $$\begin{align} S &\to aSD \;|\; bB \\ D &\to dS \;|\; a \\ B &\to bB \;|\; ...
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46 views

Create a finite-state machine

I need to create a finite-state machine which accepts strings whose characters are in {a,b,c} and produce output strings of T's and F's. The machine outputs a T once the characters ab is encountered ...
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61 views

Proving context free language membership is $P$ complete with respect to log-space reductions

This is exercise from Introduction to Automata theory, Languages and Computation, by Hopcrof, Ullman (first edition). I found example of polynomial reduction to some problems in logic, or graph ...
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46 views

Minimal DFA for a given regular expression

How can I construct a minimal DFA from the following definition? $L=\{w \in \{a,b,c\}^* $: if the second-to-last letter from w is an $a$, then the number of $c$'s $\le 1\}$ I've already made a ...
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59 views

Prove the following by using mathematical induction

If we define the alphabet such that $$ \Sigma = {\{a,b}\} $$ and let $w$ be a string over it. I'd like to prove $$ ( \operatorname{comp}(w))^R = \operatorname{comp}(w^R) $$ where $$ w^R$$ and ...
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23 views

Can the NFA constructs be minimized?

When converting a regular expression to a NFA you need to use certain constructs. My question is can these constructs be minimized? We have one with 4 states, I want to use the one with 2 states ...
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47 views

Theory of Automata concepts

I just started taking Theory of Automata and I'm having a hard time understanding some of the concepts. It's been only a week and the following questions are my homework. I'm not asking you to do my ...
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46 views

Extended PDA vs TM

We studied in class that PDA is less powerful than TM. My question is: Extended PDA : for every $\alpha,\beta \in \Gamma \cup \{\epsilon\}$, $\sigma \in \Sigma \cup \{\epsilon\}$, $q,r \in Q$, $w ...
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44 views

Language requiring a DFA with a certain number of states to implement

For any function $f\colon\{0,1\}^n\to\{0,1\}$, define a language $S_f = \{(b_1,b_2,\ldots ,b_n)\in\{0,1\}^n : f(b_1,b_2,\ldots ,b_n) = 1\}$. So all words in the langugage has same length $n$. I have ...
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92 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 ...
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54 views

Turing Machines

Suppose that $\Sigma$ is a finite set and that $L_1$, $L_2$ and $L_3$ are Turing acceptable subsets of $\Sigma^*$ that satisfy the following properties: $L_1 \cup L_2 \cup L_3 = \Sigma^*$; $L_1 \cap ...
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49 views

$DFA/NFA$ for $L(OPPOSITE)=\{uv:vu\in L\}$

I'm trying to prove that: $L(OPPOSITE)=\{uv:vu\in L\} \in L_{FA}$ given that: $L \in L_{FA}$ . I'm trying to construct a finite automata that accepts $L(OPPOSITE)$ in order to prove it but I got ...
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86 views

Constructing an NFA accepted by a grammar

Contruct an NFA of the language accepted by the grammar below. $$G=(\{S,A,B\}, \{a,b,c\},S,P)$$ $P: S\rightarrow abaS\ \ | \ cA\\ \ \ \ \ \ \ A\rightarrow bA\ \ | \ cB \ \ | \ aa\\ \ \ \ \ \ ...
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19 views

Given two minimal FSMs with one accepting a subset of the other, must a simulation exist?

As part of an example, Abstract and Concrete Categories, section 3.35, claims: For every two minimal [by number of states] $\Sigma$-acceptors $A$ and $A'$, there exists at most one simulation $A ...
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160 views

PDA state diagram with an inifinite languge but with no looping states

For class I'm supposed to create a PDA state diagram that is capable of generating an infinite language with no state q such that q is reachable from the start state, there is no cycle within the ...
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115 views

Mathematical formulation of 'Indra's net'

Quoting Wikipedia: "Imagine a multidimensional spider's web in the early morning covered with dew drops. And every dew drop contains the reflection of all the other dew drops. And, in each ...
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193 views

Confusion related to state equivalence of finite state machines

I have this confusion if there are two states of a machine p and q. Let x be an input string such that length of x = k, g be the output function and let g(p,x) and g(q,x) be the output when the input ...
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33 views

Why Algorithm is not is exist for understanding RE

I am reading Daniel I. Cohen book of computer theory. Here, he wrote that the recursive definition of regular Expression is easy to interpret a language, However, don't provides the way how to ...
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11 views

Turing machine that modifies each cell that contains a certain input one time at most

If I have a single tape turing machine running on some input $x$, where it modifies each part of the tape with $x$ one time at most...would the TM be decidable? Any advice or guidance appreciated; ...
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12 views

What is sense of $In(\phi)$ in Rabin's theory of SO-decidability?

In M.O. Rabin's article Decidability of second-order theories and automata on infinite trees in section dedicated to automata on infinite trees there is definition of $In(\phi)$ function: For a ...
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51 views

Formal Languages and Automata proof

$L$ and $K$ are subsets of $A^*$ where $A$ is an alphabet. Prove that $(L^* K^* )^* = (L \bigcup K)^*$ where $L^*=(L^0)\bigcup (L^1)\bigcup (L^2)\bigcup \ldots$ and ...
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24 views

How do I show language of composite number of x's not context-free?

I want to know if {0^k | k is a composite number} a context free language?? If , it's not,can anyone give me its proof by pumping lemma, I'm just unable to figure it out..
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12 views

Constructing a nondeterministic automaton from deterministic

Construct a nondeterministic finite-state automaton that recognizes the language generated by the regular grammar G = {V,T,S,P} where V = {0,1,S,A,B}, T = {0,1}, S is the start symbol, and the set of ...
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13 views

Converting the NFA produced from the language $a^nb^n : n\geq 0$ to a DFA to show its regular? Leading to question about pumping lemma.

I am reading about the pumping lemma, and having a hard time understanding it. I noticed that it is used to prove a language is not regular by contradiction. So you must first prove that a language in ...
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12 views

Showing that $f(K) = {f(a) : a ∈ K}$ is recursively enumerable

Today we went over things that are recursively enumerable, but I cant seem to grasp how to prove the equation $$f(K) = {f(a) : a ∈ K} $$ is recursively enumerable. I can prove that equations are ...
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26 views

syracuse/collatz variant

Here is a variant of the famous Syracuse/Collatz problem: if you think about the maps $n \to n/2$ and $n\to 3n+1$ as edges in a non deterministic automaton whose states are the integers, so that ...
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34 views

contradiction of pumping lemma on even palidrome language's completion

I have the language of all the words that are not even length palindromes, or more formally: $L= \{ w: \forall u\in\Sigma^*, w\ne uu^r \}$. And I need to prove that the Pumping Lemma for regular ...
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77 views

DFA for language accepting odd number of a's and each a followed by at least 3 b's

I am creating a DFA for a language (over alphabets {a,b}) that accepts all strings containing "odd number of a's and each a followed by at least 3 b's" . This is what I've gotten so far with q4 as the ...
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37 views

Number of states of a finite automaton recognizing all words beginning with some fixed string $x$

For a string $x \in \{a,b\}^\ast$ with $|x| = n$, how many states are required for an FA accepting the language of all strings in $\{a,b\}$ that begin with $x$? For each of these states, describe the ...
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41 views

Every DPDA has an equivalent DPDA that always reads the entire input string

I am trying to understand the proof from Michael Sipser's Introduction to the Theory of Computation, page 132. I don't understand why if $q \in F′$ then $\delta(q,a,\$)$ is set to ...
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13 views

What are the classes in A.N. Maslov hierarchy of indexed languages corresponding to Chomsky Hierachy?

As we know,that classes in A.N. Maslov hierarchy of indexed languages of level 2 is in sensitive languages of Chomsky hierarchy. What are the classes in A.N. Maslov hierarchy of indexed languages ...
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23 views

Do automatons and formal grammars belong to formal systems

A formal system consists of a formal language, a formal grammar that generates the language, a set of axioms, and a set of inference rules. Are automatons also formal systems? Is an automaton ...
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112 views

How to check whether a language is regular or not?

Say I have a given expression like $L_1\{a^n\mid n\ge0\}$ $L_2\{b^n\mid n\ge 0\}$ Then what is the procedure of checking weather L1.L2 is regular or not?
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13 views

Struggling to prove Markov chain property / State machine property - I can see what I need to do just can't write it

First notation, I have created the shorthand: $$P_x(A)=\mathbb{P}(A|X_0=x)$$ just to save time. I wish to prove "Lemma 1.3" which states the following: If $0<\alpha\le P_x(T_y\le k) \forall x\in ...