Questions tagged [automata-theory]

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

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2answers
130 views

finite automata under morphism [closed]

Given two (deterministic) finite automata $A, B$ over $\Sigma$, a mapping $h:\Sigma\rightarrow \Sigma'$ Naturally $h$ can be extended to a mapping in $\Sigma^*\rightarrow \Sigma'^*$ which is denoted ...
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1answer
166 views

What language $L \in NCM$ has $\overline{L} \not \in NCM$?

$NCM$, the class of non-deterministic reversal-bounded counter machines, has a lot of interesting dependability and closure properties. It's known that, unlike the deterministic version, NCM is not ...
3
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1answer
300 views

Deterministic Büchi + its complement covers LTL?

It is well known that deterministic Büchi automata (DBA) are less expressive than non-deterministic Büchi automata (NBA), and in particular DBA are not enough to cover linear temporal logic (LTL). ...
10
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2answers
276 views

The number of states of local automata

A deterministic automaton $\mathcal A = (X, Q, q_0, F, \delta)$ is called $k$-local for $k > 0$ if for every $w \in X^k$ the set $\{ \delta(q,w) : q \in Q \}$ contains at most one element. ...
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11answers
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Books on automata theory for self-study

I need a finite automata theory book with lots of examples that I can use for self-study and to prepare for exams.
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2answers
162 views

Are deterministic context-free languages closed under outfix (or other erasing operations)

Define the outfix of a language $L$ to be $Outf(L) = \{xy \mid \exists z. xzy \in L \}$. Are any known results about whether deterministic context-free languages are closed under this operation, or ...
4
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1answer
253 views

What characterizations exist for the grammars that can express subsets of the context-free languages?

It is well known that CFGs and PDAs are equivalent, and there has been extensive research about the relationship between deterministic pushdowns and $LR(1)$ grammars, as $DCFL$ is a subset of $LR(1)$. ...
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2answers
122 views

Looking for menu-driven coding editor based on a programming language state machine [closed]

I'd like to know whether an application development environment exists that uses a menu-driven coding editor that employs a programming language state machine. This would mean that commands, variable ...
16
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1answer
426 views

Can constant ambiguity reduce the state complexity of a regular languages?

We say that NFA $M$ is Constantly Ambiguous if there exist $k\in \mathbb{N}$ such that any word $w\in \Sigma^*$ is accepted by either $0$ or (exactly) $k$ paths. If automaton $M$ is constantly ...
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3answers
253 views

Regular languages under change of encoding

Consider a regular language $L$ with alphabet $\Sigma = \{0,1\}$. Can we say that the set of strings in $L$ (representing non-negative integers in binary encoding) when represented in some other ...
8
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1answer
368 views

Lower bound for NFA accepting 3 letter language

Related to a recent question (Bounds on the size of the smallest NFA for L_k-distinct) Noam Nisan asked for a method to give a better lower bound for the size of an NFA than what we get from ...
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0answers
86 views

Which paper first showed that any context-free grammar (CFG) is equivalent to some CFG in Chomsky normal form?

Which paper first showed that any context-free grammar (CFG) is equivalent to some CFG in Chomsky normal form? I cannot find an reference.
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1answer
459 views

Theta functions of automata relations

Let $A,B$ be two automata over the same alphabet $\Sigma$; they are supposed to be complete, strongly connected DFAs. We denote by $._A$ (resp. $._B$) the action induced by $\Sigma^*$ over $Q(A)$, i.e....
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1answer
248 views

is determining an unknown CFL from intersection of two CFLs decidable?

this problem was asked over a week ago on cs.se now with 7v and no answers so far, ie still "open". (there are many somewhat related problems/near variants re CFLs but its not obvious how to reduce it ...
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2answers
741 views

Bounds on the size of the smallest NFA for L_k-distinct

Consider the language $L_{k-distinct}$ consisting of all $k$-letter strings over $\Sigma$ such that no two letters are equal: $$ L_{k-distinct} :=\{w = \sigma_1\sigma_2...\sigma_k \mid \forall i\in[k]...
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2answers
233 views

A tool for minimal NFA computation

It is well known that minimizing an NFA for a fixed regular language is $PSPACE-Complete$. As far as I know, there are no better than trivial algorithms for minimizing such NFA, but there's a little ...
6
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1answer
161 views

Inverse of transducer compositions

Consider a Generalized Sequential Machine (GSM; or nearly equivalently -- an FSM transducer). These machines are closed under compositions. A composition of two GSMs $f(x)$ and $g(x)$ can be written ...
11
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1answer
283 views

Can one-way alternating automata with one-counter recognize some unary non-regular languages?

One-way alternating pushdown automata (1APDA) can recognize any language in $ DTIME(2^{O(n)}) $ (Alternation by Chandra, Kozen, and Stockmeyer, 1981). By replacing a pushdown storage of a 1APDA with a ...
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1answer
357 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 ...
5
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1answer
276 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? ...
1
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1answer
307 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
540 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 ...
7
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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. ...
3
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0answers
116 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
76 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
414 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 ...
4
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1answer
252 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
531 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 ...
3
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0answers
171 views

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, ...
6
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0answers
496 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 ...
4
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0answers
84 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
624 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 ($...
3
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0answers
111 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 \...
11
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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 ...
0
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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
456 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 ...
3
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0answers
105 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(\...
0
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1answer
179 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 $P \subseteq L$?
5
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3answers
651 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 ...
2
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1answer
533 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 ...
4
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3answers
470 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 ...
1
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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 ...
3
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0answers
218 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 ...
10
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1answer
365 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
792 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 ...
7
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3answers
650 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 ...
7
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0answers
143 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
238 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 ...
6
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0answers
179 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
150 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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