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Questions tagged [automata-theory]

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

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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 ...
Michaël Cadilhac's user avatar
16 votes
0 answers
450 views

Is this problem on unambiguous finite automata NP-complete?

An unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path. In this post, for $n\in \mathbb{N}$, what I call an $n$-UFA (resp....
M.Monet's user avatar
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14 votes
0 answers
210 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 ...
Abuzer Yakaryilmaz's user avatar
13 votes
0 answers
217 views

Regular languages accepted by an automaton with at most one transition per letter

I'm interested in the (very restricted) subset of regular languages for which there is an automaton having the following property: for every letter $a$ of the alphabet, the automaton has at most one ...
a3nm's user avatar
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13 votes
0 answers
353 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 ...
Huck Bennett's user avatar
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11 votes
0 answers
185 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 ...
Taylor Dohmen's user avatar
10 votes
0 answers
164 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 ...
Michaël Cadilhac's user avatar
9 votes
0 answers
110 views

Expressiveness of pushdown automata whose stack height sequence is unambiguous

I consider pushdown automata on an alphabet $\Sigma$, which are intuitively finite automata with a stack. Formally, a pushdown automaton $A = (Q, q_0, F, \Gamma, \Delta)$ is a finite set $Q$ of states,...
a3nm's user avatar
  • 9,449
9 votes
0 answers
123 views

Reference request: DFA linear-time minimization

What is the most complicated kind of deterministic finite-state automaton that can be minimized in $O(n)$ time? Here’s what I’ve been able to find so far: The acyclic case has been solved. So any ...
ShyPerson's user avatar
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9 votes
0 answers
295 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 ...
ghosts_in_the_code's user avatar
9 votes
0 answers
642 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 ...
misberner's user avatar
  • 191
8 votes
0 answers
158 views

Determining if transducer automaton has two states with intersecting images, 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 ...
grok's user avatar
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8 votes
0 answers
2k 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 ...
Fasermaler's user avatar
8 votes
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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 $2 \times 10^6$ ...
Lucas Alves's user avatar
7 votes
0 answers
111 views

Deciding whether DCFG is visibly pushdown

Is the following problem decidable? If so, what's the best algorithm known? Instance: a deterministic pushdown automaton $A$ Question: Does there exist (i) some partition of the alphabet into push, ...
Antimony's user avatar
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7 votes
0 answers
156 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 ...
042's user avatar
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0 answers
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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 ...
kbkb's user avatar
  • 171
7 votes
0 answers
374 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 ...
vzn's user avatar
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6 votes
0 answers
117 views

How to prove clock equivalence is a time-abstracted bisimulation

An important step of developing the theory of timed automata is to reduce the question of reachability in the timed automata, which has infinitely-many states, to the question of reachability in an ...
generic_logician's user avatar
6 votes
0 answers
75 views

Updating (minimal) DFA incrementally

Is there algorithm to incrementally update (minimal) DFA? Namely, having relatively large minimized DFA I want to update it incrementally using union and sudtraction with other (relatively small, ...
gsv's user avatar
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6 votes
0 answers
128 views

What is the Simplest type of automaton that can simulate all DFAs?

During recent research in a somewhat unrelated field (Spin Physics), I stumbled across a subclass of regular languages. The context of the research poses the question what the minimal power of the ...
Thomas Tappeiner's user avatar
6 votes
0 answers
717 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 ...
Dave Lang's user avatar
6 votes
0 answers
207 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 ...
vincenzoml's user avatar
6 votes
0 answers
162 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 ...
domotorp's user avatar
  • 14k
6 votes
0 answers
286 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?...
a3nm's user avatar
  • 9,449
5 votes
0 answers
80 views

Equivalent Characterizations of Semilinear Sets

Coming from an automata theory background, the semilinear sets seem like an ideal candidate for having lots of equivalent characterizations. I am already familiar with a few well known ones: Sets ...
TomKern's user avatar
  • 489
5 votes
0 answers
157 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 ...
Joseph O'Rourke's user avatar
5 votes
0 answers
112 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 ...
Alex R's user avatar
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0 answers
128 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 ...
user avatar
5 votes
0 answers
250 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 ...
Gianluca Mezzetti's user avatar
4 votes
0 answers
97 views

Higher dimensional automata?

An NFA is just the data of a labelled, directed multigraph with a accepting predicate over the vertices. Simplicial sets generalize directed multigraphs by allowing the existence of higher dimensional ...
Steven Schaefer's user avatar
4 votes
0 answers
94 views

Linear-time maze exploration for finite automaton with pebbles?

Blum and Kozen have shown that a robot with the computational capabilities of a finite automaton can visit all $n$ cells in a quadratic maze when the robot is equipped with two pebbles which it may ...
jfriemel's user avatar
4 votes
0 answers
123 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 ...
kafka's user avatar
  • 349
4 votes
0 answers
101 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.
ghosts_in_the_code's user avatar
4 votes
0 answers
93 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 ...
damned's user avatar
  • 141
4 votes
0 answers
270 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 ...
Aadit M Shah's user avatar
3 votes
0 answers
119 views

State-based vs. transition-based definitions of alternating automata

Maybe this is a naïve question but I'm having difficulties finding the answer in the literature. Alternating finite automata (AFA) are usually defined in modern literature in the following terms. An ...
Nicola Gigante's user avatar
3 votes
0 answers
156 views

Deciding whether an arbitrary context-free grammar generates a deterministic push-down automata?

I know that it's undecidable whether an arbitrary context-free grammar is ambiguous, but is it decidable whether that grammar is deterministic? I can't find the answer to this question anywhere on the ...
Joshua Wise's user avatar
3 votes
0 answers
137 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?
bitconfused's user avatar
3 votes
0 answers
116 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 ...
Antimony's user avatar
  • 917
3 votes
0 answers
110 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 ...
catalyst's user avatar
3 votes
0 answers
110 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 ...
Devendra Bhave's user avatar
3 votes
0 answers
103 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 ...
StefanH's user avatar
  • 2,077
3 votes
0 answers
149 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 ...
R B's user avatar
  • 9,458
3 votes
0 answers
121 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. ...
D. Chen's user avatar
  • 103
3 votes
0 answers
176 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, ...
R B's user avatar
  • 9,458
3 votes
0 answers
115 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 \...
StefanH's user avatar
  • 2,077
3 votes
0 answers
246 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 \...
C.E.Sally's user avatar
  • 313
3 votes
0 answers
310 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 ...
Chad Brewbaker's user avatar
2 votes
0 answers
79 views

Im looking for papers to read to strengthen my understanding of overall cs theory

I took automata theory and the things we learn in that class interest me a lot and am looking to read more papers to take a deeper dive into cs theory if any of y'all have any paper suggestions that ...
Emre Guzelordu's user avatar