Questions tagged [automata-theory]

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

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19
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472 views

To what extent MSO = WS1S, when adding relations?

[This question has been asked on MathOverflow with no luck a month ago.] Let me first clarify my definitions. For a word $w \in \Sigma^*$, with $\Sigma =\{a_1, \ldots, a_n\}$, I define two ...
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207 views

The best known upper bound for two-way probabilistic finite automata with one-counter

It is known that the class of languages recognized by two-way deterministic finite automata with one-counter (2D1CAs) is a proper subset of $ \mathsf{L} $ (deterministic log-space): A 2D1CA can run at ...
12
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297 views

Survey on infinite alphabet automata?

The paper "Symbolic Finite State Transducers, Algorithms and Applications" by Bjorner et al (to appear at POPL 2012) describes one type of finite-state, infinite-alphabet automata/transducers by using ...
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300 views

Can we approximate the number of words accepted by an NFA?

Let $M$ be an acyclic NFA. Since $M$ is acyclic, $L(M)$ is finite. In a related question, it was suggested that exact counting of the number of words accepted by $M$ is $\#P$-Complete. The second ...
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111 views

Are there cascade decompositions of machines that are more general than finite automata?

The idea of decomposing automata and their associated semi-groups into irreducible sub-components is due to Krohn & Rhodes and has been explored relatively thoroughly. Krohn & Rhodes gave an ...
10
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145 views

A language outside the Boolean closure of stochastic languages

Stochastic languages, that is, those accepted by probabilistic automata, are known to not be closed under intersection, union, concatenation, and morphism, even on unary languages. I have two ...
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261 views

A super-linear time problem in NL

It is a well-known fact that $ \mathsf{NL} = \cup_{k>0} \mathsf{2NFA[k]} $, where $ \mathsf{2NFA[k]} $ is the class of languages recognized by two-way nondeterministic finite automata with $ k>0 ...
9
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162 views

Shortest string in the intersection of regular languages

Inspired by https://codegolf.stackexchange.com/questions/53310/shortest-universal-maze-exit-string Each of the 138,172 valid mazes can be represented as a DFA with 9 states (including starting and ...
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492 views

What exactly are Moore machines?

Ok, don't be scared by the title - it is not that I don't know the concept of a Moore machine, or basic FSM concepts in general. However, I think that the term "Moore machine", despite being ...
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1k views

Data structures for Finite Automata

I am a Control Engineer and I have been working on Discrete Event Systems and Supervisory Control, based on Finite Automata Theory. My problem is to represent large automata (about $2 \times 10^6$ ...
7
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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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150 views

Size complexity of probabilistic two-way automata for a Boolean function

I'm interested in computing Boolean functions $f:\{0,1\}^n\rightarrow\{0,1\}$ with two-way finite automata and I will measure the complexity of a Boolean function by the number of states for the ...
7
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336 views

Examples of non-CSLs not created through diagonalization

Hopcroft & Ullman 1979, Intro to Automata Theory, Languages, & Computation states (p. 224) that "almost any language one can think of is CSL; the only known proofs that certain languages are ...
6
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1k views

What would a PDA be with a queue instead of a stack?

A while ago it occurred to me that the stack data model in a push-down automaton could be exchanged for a queue or deque model. I've explored this a bit as a pet project and it looks like an automaton ...
6
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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 ...
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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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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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273 views

Language of stack configurations of a pushdown automaton

Consider a pushdown automaton $A$ with stack alphabet $\Gamma$. Let $L$ be the language on $\Gamma$ of the stack configurations encountered during accepting runs of $A$. Is $L$ a context-free language?...
5
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111 views

Languages whose Parikh image is recognizable

Let $\Sigma$ be some alphabet, and $p : \Sigma^* \to \mathbb N_0^{|\Sigma|}$ the Parikh map. A formal language $L \subseteq \Sigma^*$ is called a slip-language, if $p(L)$ is a semilinear set. By ...
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143 views

Mastery-based grading for Theory of Computation

I would be interested to learn of anyone's experience using mastery-based (or "mastery-level") grading in a Theory of Computation course. Usually this requires—at a minimum— a detailed ...
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98 views

Why do multi-stack visibly pushdown languages label each call/return with a particular stack?

In A Unifying Approach for Multistack Pushdown Automata, multistack visibly pushdown automata are defined in terms of an alphabet where each symbol is either a call or return for a particular stack or ...
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116 views

Learning Finite Automata Behavior by Experimentation

This conjecture is from an expert in Game Theory area, I post it here to draw more attentions of TCS experts. Discussions and comments are welcome. http://gtcenter.org/WCS_Call_for_papers.pdf An ...
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49 views

Translation from LTL with Past to LTL

Has it been charaterized the cost of the translation from LTL with Past to LTL? In [Gab89] this translation is assumed to be non elementary and in "Temporal Logic with Past is Exponentially More ...
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77 views

Libraries for programming automata and Turing machines

What are the most useful libraries around for coding related to automata and Turing machines? By useful I mean the number of functions and algorithms supported by it.
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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 ...
4
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231 views

Intersection between register automata and pushdown automata over infinite alphabet

I'm not an expert in automata theory, this is a reference request. As far as I have understood it is known in the automata comunity that register automata by Kaminski are closed by intersection with ...
4
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1answer
334 views

Is it known if $CFL \subseteq NSPACE(o(log^2(n)))$?

$CFL$ is the class of context-free languages. Question Is $CFL$ known to be solvable in $o(log^{2}(n))$ non-deterministic space? What about $DCFL$?
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29 views

Determining if transducer automaton is non-minimal without minimizing?

I work (in implementation!) with deterministic finite state automata with input and output; i.e. there are transitions (start state,input letter)$\to$(new state,output letter). Thus every state gives ...
3
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123 views

Weakest model of computation that can typecheck?

What's the weakest (known) model of computation (or smallest language class) that can decide whether a simply-typed lambda calculus program type checks? What about an (explicitly typed) CoC program?
3
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39 views

Incremental PDA emptiness testing?

Is there anything known about the problem of incremental emptiness testing for a pushdown automata? Suppose you have a PDA with (up to) $n$ states and transitions, but instead of being given the ...
3
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85 views

Characterization of deterministic pushdown automata

Is there any known characterization for deterministic pushdown automata (DPDA)? For example, visibly pushdown automata(VPA) is a subclass of DPDA, which is characterized by following syntactic ...
3
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93 views

Looking for a specific tree automata model

is there any tree automata model over unranked trees (that is with unbounded number of children for each node), such that: Checking non-emptiness and universality is decidable in elementary time, ...
3
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82 views

A question on the introduction of the Wagner hierarchy from K. Wagner's original paper

My question is related to the seminal paper On $\omega$-regular sets by K. Wagner, which introduced a hierarchy which is now know as the Wagner- (or Wadge-) hierarchy of $\omega$-regular sets. In ...
3
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238 views

Equivalence of deterministic finite transducers over finite/infinite words

Equivalence of deterministic finite transducers - a special case of single-valued finite transducers - is decidable because it is decidable whether a transducer is single-valued. Note that two ...
3
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144 views

Restricted-Input Automaton

In the classic setting, an automaton for a language $L$ is required to accept all words in $L$ and reject/get stuck on every word in $\Sigma^*\setminus L$. All of the related concepts are then ...
3
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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. ...
3
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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, ...
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 \...
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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(\...
3
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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 ...
3
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232 views

Providence of pumping lemmas for regular languages

I'm looking to track down who discovered the following pumping lemmas for regular languages. (where $p$ is the pumping constant.) Reg($L) \rightarrow \exists p\forall w(\in L) \forall u_1u_2v(\in \...
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306 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 ...
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67 views

Proof: Why are MM-1QFA strictly more powerful than MO-1QFA? // Quantum automata

While dealing with quantum finite automata (QFA), I repeatedly come across the statement that measure-many QFA (MM-1QFA, KW97) are strictly more powerful than measure-once QFA (MO-1QFA, MC97). More ...
2
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0answers
101 views

Notion of “quotient” or “inverse” for recognizable tree languages?

Related to my previous question but this time I have a better idea of what I'm actually asking. I'm looking at the following operation on recognizable tree languages (i.e. regular tree grammars, ...
2
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0answers
54 views

Regular Tree Languages are closed under quotient?

The Wikipedia page for Regular Tree Grammars notes that if $L_1$ and $L_2$ are regular tree languages, than $L_1 \setminus L_2$ is as well. However, it doesn't define this quotient operation for trees,...
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0answers
89 views

Proof of the equivalence of Muller automata and Parity (or Rabin chain) automata

Let $A$ be some finite alphabet and $\mathcal A = (Q, \delta, q_0)$ be some determinisitic finite automaton. Then $\mathcal A$ accepts infinite words $\xi \in A^{\omega}$ according to the Muller ...
2
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0answers
78 views

What is the class of the languages recognized by PCREs?

I have been considering building a tool that would convert regexes between the various syntaxes (BRE, ERE, PCRE). It is obvious that PCREs are too strong for the is-regular problem to be decidable, ...
2
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0answers
196 views

Complexity of DBA-recognizable Omega-Languages

Given an $\omega$-regular expression $r$, how difficult is it to decide if $L(r)$ is recognizable by some deterministic Büchi automaton? I know it is solvable in EXPTIME by converting the regular ...
2
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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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0answers
777 views

What is the relationship between the number of states in Quantum Finite Automata and the number of non-regular languages they can recognize?

It is has been shown that Quantum Finite Automata can recognize at least some non-regular languages. What is the relationship between the number of states in a qfa and the number of non-regular ...