Questions tagged [automata-theory]

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

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346 views

Are finite state automata with one register storage equivalent to push down automata?

This is a very simple question, but I couldn't find a reference and I just wanted to check my facts. I was looking for a state machine similar to pushdown automata but where the stack is restricted to ...
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1answer
272 views

Equivalence problem for one-counter automata

I know that the equivalence problem for deterministic one counter automata is decidable, however does anyone know whether it is decidable for all one counter automata or just the deterministic ones? ...
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650 views

Büchi automata with acceptance strategy

The problem Let $A=\langle \Sigma, Q, q_0,F,\Delta\rangle$ be a Büchi automaton, recognizing a language $L\subseteq\Sigma^\omega$. We assume that $A$ has an acceptance strategy in the following sense ...
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1answer
281 views

On equivalence of NLBA and DLBA

Where I can find reference and documents on the work made for proving whether DLBA are equal NLBA nr not? What is the underlying problem? Why it is still an open question in TCS?
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1answer
501 views

What are good conferences for algorithms about finite automata?

I am writing a research paper, which describes some properties about finite automata. It also provides a couple of algorithms that can measure some aspects of the properties. Could you point out some ...
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2answers
8k views

Difference between infinite state machines and turing machines

Finite state machines (FSM) are strictly less powerful than turing machines (TM). But this is not the case with infinite state machines (ISM). For example, every TM can be embedded into some ISM. ...
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0answers
115 views

Concentration of Stationary Distribution on Random Directed Graphs

We consider a random directed graph with fixed out-degree $d$. Each vertex chooses $d$ neighbors with replacement, uniformly and independently. Self-loops and multiple arcs are allowed in this model. ...
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0answers
74 views

WFSA over hyperreals

Are there any works where authors tried to define weighted finite state automata over hyperreals (or a similar object allowing for infinite and infinitesimal values) in an attempt to make automata ...
2
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1answer
394 views

Computing the Syntactic Congruence

The syntactic monoid of a language $L \subseteq X^*$ is defined as the monoid obtained from the congruence relation $$ u\ \tilde{}\ v \ \mbox{ iff }\ \forall x,y \in X^* : xuy \in L \leftrightarrow ...
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1answer
233 views

The polynomial languages and ordered syntactic monoids

A polynomial language is a languge which could be represented as the finite union of languages of the form: $$ A_0^* a_1 A_1^* a_2 \cdots a_k A_k^* \quad a_i \in X, A_i \subseteq X $$ Such an ...
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3answers
529 views

Can words in regular languages be generated by automata in a unique way?

If $L\subset \Sigma^\ast$ is a regular language then it is known that we can find a directed graph (aka automaton) $G$ with edges labelled with symbols from $\Sigma$, an ‘initial’ vertex, and a set of ...
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Deciding whether a binary multiplicity automaton has empty language

Multiplicity automatons (see here) is an interesting model. They have the (almost) same syntax as a non-deterministic finite automatons, but instead of deciding whether a word belongs to a language, ...
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1answer
377 views

Adherence of languages and the Dyck language

Let $L \subseteq X^*$ and $X = \{a,b\}$ be a language of finite words, denote by $A(u)$ the prefixes of some word (finite or infinite), then the adherence $\mbox{Adh}(L)$ is defined to be the set of ...
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475 views

Generalized sequential machine synthesis subject to language equivalence/inclusion and reachability

A generalized sequential machine (GSM) is a generalization of a Mealy machine where on each transition one input symbol is read and 0 or more output symbols are written. As in a Mealy machine, we ...
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82 views

Sub optimal regex equivalence

Regex Equivalence is a hard problem which in general takes exponential space and exponential time. Are there any approximation/sub-optimal algorithms with some theoretical guarantees over equivalence ...
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1answer
597 views

Intersection between context-free and context-sensitive language decidability [closed]

I'm trying to find a formal proof of the following fact: Given a context-free language, say $L_1$, and a context-sensitive language, say $L_2$, it is NOT decidable if their intersection is empty ($...
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0answers
110 views

Transfering properties from subsets of $X^*$ to subsets of $X^{\omega}$ by using the topology induces by Cantor space

A language $L \subseteq X^*$ is non-counting of order $n > 0$ iff for all $u,v, w \in X^*$ $$ uv^nw \in L \Leftrightarrow uv^{n+1} w \in L. $$ A $\omega$-language (set of infinite sequences) $L \...
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2answers
4k views

2DFA that requires many states in equivalent DFA?

Is there a 2DFA with $n$ states (where $n$ is nontrivial, say at least 4) that requires at least $2^n$ states to simulate using any DFA? A two-way DFA (2DFA) is a deterministic finite-state automaton ...
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1answer
86 views

Difference between locally testable and it's boolean closure

A language $L$ is called i) locally testable in the strict sense iff there exists $P, S, I \subseteq X^*$ such that $$ w \in L \mbox{ iff } pref^k(w) \in P, suffix^k(w) \in S, infix^k(w) \subseteq I....
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4answers
429 views

Questions about regular languages and their sublanguages

I am interested in the following questions and would be grateful if anyone could give me hints or point me to articles: 1) Given a regular language $L$, what are its regular sublanguages $L'\subseteq ...
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104 views

Subsets of $\omega$-words which share certain factors and languages accepted by special (prefix-closed) automata

Let $\mathcal A$ be an automaton, then I define the following $\omega$-language accepted by $\mathcal A$: $$ L'(\mathcal A) := \{ \eta \in X^{\omega} : v \sqsubset \eta \mbox{ implies } v \in L(\...
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1answer
173 views

Does every regular language contains a strictly locally testable language?

Let $L$ be an infinite regular language, then does there exists a strictly locally testable infinite language $P$ such that $P \subseteq L$?
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1answer
108 views

When does a set of infixes determine a set of ($\omega$-) words

If a have a set of finite infixes of a specific length, which $\omega$-languages are determined by them, and furthermore, when does a set of infixes determine a $\omega$-word uniquely. For example for ...
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3answers
640 views

Formal definition of parser?

I'm looking for an accepted, formal definition of a parser as function $f$ returning an AST, but I cannot find any reference in literature; all I can find is the definition of a recognizer as a ...
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1answer
519 views

Closure Properties of Locally Testable Language

Are locally testable languages closed under complementation? I guess yes, because when I can decide membership by sliding a window of size $k$ over the word and looking if the $k$-length words ...
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14answers
22k views

How practical is Automata Theory?

There is always a way for application in topics related to theoretical computer science. But textbooks and undergraduate courses usually don't explain the reason that automata theory is an important ...
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3answers
437 views

How to minimize a FSM transducer?

In contrast to FSM minimization which is well studied with various algorithms, theorems and has many practical applications, I'm looking for any nontrivial insight, analysis and references to the ...
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0answers
94 views

Properties of the number of copies of an NFA in each state

For an NFA $A$ with $n$ states and a word $w$, we can associate an $n$-dimensional vector $v_w$ with entries in $\mathbb{N}\cup\{0\}$ denoting the number of copies of the NFA in each state after ...
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0answers
213 views

Learning about Nested Stack Automata

I want to learn about nested stack automata. However my efforts to find a suitable learning resource have so far been abortive: The Wikipedia article on nested stack automata is a stub. Alfred Aho's ...
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1answer
339 views

Multi-language DFA minimisation

I'm interested in a slight generalisation of DFA. As usual we have state-set $Q$, finite alphabet $\Sigma$, a $\Sigma^*$-action defined on $Q$ by $\delta : Q\times\Sigma\rightarrow Q$, and initial ...
14
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3answers
746 views

The significance of state complexity in automata and regular languages?

I'm reading "Concatenation of Regular Languages and Descriptional Complexity" by Galina Jiraskova, 2009 on the state complexity resulting from concatenation of two regular languages ( by Galina ...
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1answer
310 views

Can I show algebraically that this regular expression accepts all binary strings?

The task is to prove that (0+1)* and 0*(1.0*)* are equivalent. 1. http://rubular.com/r/K9Hp9tU6px 2. http://rubular.com/r/N8VpoEcch4 EDIT: Forgot that + was ambiguous here! I want to prove that the ...
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3answers
607 views

Algorithm for ranking members of a regular language?

A little while back, I was reading a paper that mentioned a method for computing an integer 'rank' for a particular string $s \in L$ where $L$ is some regular language. This rank uniquely determines ...
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0answers
141 views

Has a result of Book and Greibach on Quasi-Realtime languages been improved?

Quasi-realtime languages are defined as languages accepted by nondeterministic multitape Turing machines in quasi-real time. Ronald Book and Sheila Greibach have shown in their 1970 paper that every ...
7
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1answer
230 views

Measurability of an $\omega$-regular language

It the previous question of mine I put a reference which shows that any $\omega$-regular language over the alphabet $\Sigma$ is a Borel subset of $\Sigma^\omega$. I am not sure whether the reference I ...
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178 views

Separation of the states of a deterministic omega-automaton by looping words taken from a regular language of non-empty words

Consider a deterministic transition structure having states in set $X$ and transition function $\rightarrow$, and an initial state $x \in X$. This structure is intended to be part of an automaton ...
6
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0answers
148 views

Are k+1 heads better than k for multiread finite automata?

Consider the deterministic (resp. non-deterministic) one-way finite automaton that is defined in the usual way except that it has k heads and in each step can decide which head to move. (It is allowed ...
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72 views

Vector representation of probabilistic automaton

Suppose we have $N$ states $q_i$, $0\leq i<N$ Suppose we have $N\times N$ probability matrix $p_{ij}$, $0\leq i<N$, $0\leq j<N$, And suppose a machine, which is being in state $q_i$ then ...
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1answer
107 views

Is it decidable whether the langauge accepted by a reversal-bounded counter machine is deterministic?

I'm wondering if anyone can point me to either an algorithm or an undecidability proof for the following question: Given a non-deterministic reversal-bounded multicounter machine $M$, is there some ...
4
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1answer
731 views

Minimal context-free grammar for a regular language

Are there any algorithms for solving exactly the following question? Given a regular language L, represented as a finite automaton say, what is a CFG with minimal number of nonterminals that generates ...
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2answers
419 views

Unary languages recognized by two-way deterministic counter automata

2dca's (two-way deterministic one-counter automata) (Petersen, 1994) can recognize the following unary language: \begin{equation} \mathtt{POWER} = \lbrace 0^{2^n} \mid n \geq 0 \rbrace. \end{...
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3answers
422 views

Simplification of weighted NFA

What options does one have for the simplification (meaning reduction in the number of states) of weighted NFA over the probability semiring? From my understanding one can determinize, and then ...
2
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1answer
97 views

Are Reversal-bounded Multicounter Machines closed under reversal?

This is a problem I have found very difficult to solve, given how the two different uses of "reversal" confuses search engines. Reversal-bounded multicounter machines are described at length in his ...
12
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1answer
331 views

Is there a book/survey-paper outlining language class hierarchies, closure properties, etc

I'm currently doing some Formal Language research involving classes of languages above Regular but below Context Free. I'm looking at things like Reversal-Bounded Multicounter Machines, Single-stack ...
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3answers
401 views

Chomsky hierarchy for tree structures

I know of the Chomsky hierarchy, which concerns the expressive power of grammars to recognize languages $L \subseteq \Sigma^*$ made of words on an alphabet $\Sigma$. Is there a similar hierarchy for ...
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1answer
305 views

Number of accepting path of a non deterministic automaton

I have a question that seems to me really natural and have probably already been studied. But keyword search on this site or google does not seems to help me to find any relevent paper. I have got a ...
7
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1answer
219 views

Complete problems and universal simulator machines

I'm trying to get straight in my mind the relation between complete problems and universal simulator machines. Some notions of computability have universal machines (Turing-computability) and some ...
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1answer
105 views

Constructing automata with the same traces, but where a CTL-formula is not equally satisfied [closed]

Hard to put this question in a short title. As part of a self-exercise, I'm trying to solve 6.15b of Principles of Model Checking by Baier and Katoen. You're supposed to prove that there does not ...
7
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1answer
1k views

Photo of «Introduction to automata…» by Hopcroft and Ullman '79 cover?

Where can I get the photo of “Introduction to automata theory, languages and computation” by Hopcroft and Ullman '79 (first edition) cover in order to be able to read all the phrases placed on the ...
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0answers
305 views

Name this digraph

I am trying to track down the name of this digraph and some references: You take all members of the transformation semigroup on $n$ elements, $T_{n}$. For two members $x$ ,$y$ ; if $x$ is in the ...