Questions tagged [automata-theory]

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

Filter by
Sorted by
Tagged with
9
votes
2answers
255 views

Bounds on this Strategy for Separating Words

Question Given binary string $z \in \{0,1\}^n$, let $f(z)$ be the smallest integer $k$ such that there exists a DFA with $k$ states, such that reading $z$ from a specific starting state, we end at a ...
14
votes
2answers
819 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 :...
11
votes
0answers
148 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 ...
1
vote
0answers
29 views

Nominal Tree Languages i.e. with Binders and Infinite Symbols?

I'm wondering if there has been any research done into automata that accept languages of trees that can bind arbitrary variables, and are considered equal under alpha equivalence. I've found so far: ...
3
votes
0answers
57 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 ...
13
votes
0answers
365 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 ...
7
votes
1answer
135 views

Isomorphism of ‘ordered’ DAGs / acyclic semiautomata

I am wondering what is known about the isomorphism problem on ordered DAGs, in particular how to find a canonical representative modulo isomorphism. By ordered I mean that each vertex has a list of ...
9
votes
0answers
84 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 ...
21
votes
2answers
3k views

computing the minimal NFA for a DFA

Many years ago I heard that computing the minimal NFA (nondeterministic finite automaton) from a DFA (deterministic) was an open question, as opposed to the vice versa direction which has been known ...
11
votes
1answer
174 views

Planarity of planar finite automata intersection

It was shown that any regular language can be specified by planar $\varepsilon$-free nondeterministic finite automaton (Bezáková, Ivona, and Martin Pál. "Planar finite automata."). Is it ...
3
votes
1answer
116 views

Rewrite relations - proof of correctness

Let $T \subseteq \Sigma^* \times \Sigma^*$ be a regular relation. We define the obligatory rewrite relation over $T$ as follows: $$ R^{obl}(T) := N(T) \cdot (T \cdot N(T))^* $$ $$ N(T) := Id(\Sigma^* ...
4
votes
1answer
126 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(\...
6
votes
0answers
191 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 ...
2
votes
0answers
203 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 ...
1
vote
1answer
119 views

What kind of computational model is the brain? [duplicate]

I was wondering what kind of computational model is the human brain (as it seems superior to a Turing machine). Another thing that should be a separate question, What would be a perfect computer model ...
8
votes
1answer
349 views

Can we efficiently enumerate the words accepted by a DFA by order of increasing weight?

Fix a deterministic finite automaton $A$ defining a regular language on the alphabet $\Sigma = \{0, 1\}$, and call the (Hamming) weight of a word $w \in \Sigma^*$ its number of $1$'s. Given a length $...
8
votes
0answers
129 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 ...
5
votes
0answers
118 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 ...
8
votes
4answers
497 views

Constraints on sliding windows

Let $L\subseteq \Sigma^*$ be a language of finite words and $n>0$ some integer. I would like to know if anything is known on the time and space complexity with respect to $n$ to check for ...
-2
votes
1answer
364 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 ...
3
votes
0answers
129 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?
6
votes
2answers
230 views

2DFA to 1DFA - Converting two way deterministic finite automata to one way deterministic finite automata

How can I convert a 2DFA to a normal DFA. Is there an algorithm/elegant way to do that ? I've been researching this for a few days but I coundn't find anything. Actually I want to implement that in ...
5
votes
1answer
160 views

Is there any equation-based method for transforming Büchi-automata to omega-regular language?

I know there exists an equation-based method for transforming finite automata into regular language (or `regular expression'). The main idea is as follows. First we construct a set of equations ...
7
votes
2answers
201 views

Closure of Recognizable Languages under Kleene Star: Algebraic Proof?

Let $Rec(\Sigma)$ be the class of languages over $\Sigma^*$ recognizable by finite monoids. To show that $Rec(\Sigma)$ is closed under Kleene star, one would usually refer to the equivalence of ...
5
votes
1answer
240 views

Name for a special family of languages?

I was wondering whether there is a standard name in the literature for the following family $\mathcal{F}$ of languages over any finite alphabet $\Sigma = \{a_1,\ldots,a_k\}$: $\mathcal{F}$ consists ...
10
votes
3answers
508 views

Maximum shortest word accepted by pushdown automata

Given a fixed alphabet, consider all deterministic pushdown automata with $n$ states that accept a nonempty language. What is the maximum length of the shortest word accepted by a deterministic ...
6
votes
1answer
93 views

What is the minimal class of subshifts for which conjugacy is known to be undecidable?

The question of whether two finite one directional shifts are conjugates is known to be decidable. The same question for sofic shifts is famously open. I have seen that some works manage to prove ...
3
votes
0answers
45 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 ...
7
votes
5answers
431 views

NP-complete decision problems on deterministic automata

Do you know any NP-complete decision problems on deterministic automata? Most NP-complete problems that come to my mind are either (see, or here) graph theoretical, or involve some string rewriting or ...
2
votes
0answers
69 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 ...
5
votes
1answer
128 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 ...
1
vote
1answer
412 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 ...
1
vote
1answer
52 views

Palindrome language and Finite Automata Machines [closed]

I'm a grad student in math. I'm unaware of available literature in theoretical computer science, so require suggestions for books. Here are the two topics I'm interested in exploring. 1) A complete ...
9
votes
1answer
165 views

Containment problem of an acyclic NFA in an NFA

Let $A$ and $B$ be NFAs, such that $A$ is acyclic. In the general case, deciding whether $L(A)\subseteq L(B)$ is $PSPACE$-hard. However, since $A$ is acyclic, we know that for every $w \in L(A)$, it ...
38
votes
14answers
24k 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 ...
1
vote
1answer
167 views

Example of a $U^\omega$ that is not Deterministic Büchi recognizable

Is there a regular language $U$, for which $U^\omega$ is not a Deterministic Büchi recognizable language. I have been thinking over it for some time, but have been unable to come up with an example.
3
votes
1answer
137 views

Intersection of two deterministic parity automata

Given two deterministic parity automata $A_1=(Q_1,\Sigma,\delta,q_{01},c_1)$ and $A_2=(Q_2,\Sigma,\delta,q_{02},c_2)$ with the finite set of states $Q_i$, the finite alphabet $\Sigma_i$, the ...
3
votes
0answers
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 ...
9
votes
1answer
429 views

Measurable language which is not $\omega$-regular

Let $\Sigma$ be a finite alphabet and let $\Sigma^\omega$ be the set of all infinite words over $\Sigma$. Consider $$ d(x,y):=2^{-\min(n \in \Bbb N_0:x_n\neq y_n)} $$ to be the metric on $\Sigma^\...
10
votes
2answers
424 views

Minimizing Automata accepting $\omega$-words (i.e. infinite words)

What is the standard approach on minimizing Büchi-Automata (or also Müller-Automata)? Transfering the usual technique from finite words, i.e. setting two states to be equal if the words "running out" ...
3
votes
1answer
92 views

Size bound on Büchi automaton for complement

For a given Büchi automaton $\mathcal A = (A, Q, \delta, q_0, F)$ we define a congruence on $A^{\ast}$ by $$ \begin{array}{llll} u \sim_{\mathcal A} v & :\Leftrightarrow & \mbox{for all }s,s' ...
11
votes
2answers
423 views

Does a given regular language contain an infinite prefix-free subset?

A set of words over a finite alphabet is prefix-free if there are no two distinct words where one is a prefix of the other. The question is: What is the complexity of checking whether a regular ...
9
votes
4answers
2k views

Proving the set of powers of 2 over ternary alphabet to be non regular.

It's simple to see that the powers of 2 over alphabet {0,1} is regular because $10^*$ is a regular expression for it. But the powers of 2 represented in ternary appears to be non regular. Pumping ...
4
votes
1answer
249 views

Are endmarkers necessary for Deterministic Pushdown Automata?

In the book by Kozen (Automata and Computability), the transition function of deterministic pushdown automata (DPDAs) is supposed, in contrast with non-deterministic pushdown automata (NPDAs), to ...
6
votes
1answer
175 views

Complexity of DFA intersection in this specific case?

In general, the size of the DFA that recognizes the intersection of $n$ languages is exponential in $n$. However, in my case I am computing the intersection of a very restricted subset of possible ...
0
votes
1answer
209 views

Where does a C-like language without heaps belong in the automata hierarchy?

Assume that the language C', unlike C, has well-defined semantics, but has similar features: pointers and manual memory management through malloc and free. Assume that C'' is the same as C' without ...
10
votes
1answer
243 views

What class of languages is recognized by finite-state automata with $k$ heads?

A DFA or NFA reads through an input string with a single head, moving left-to-right. It seems natural to wonder about finite-state machines that have multiple heads, each of which moves through the ...
4
votes
0answers
52 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 ...
1
vote
1answer
83 views

Can we have more than one Deterministic Finite Automata diagrams for a set of strings? [closed]

Much like many math equations can be simplified. I am wondering if Deterministic Finite Automata diagrams can equal each other while some may be more simplified than others. I am following the youtube ...
5
votes
1answer
133 views

Are PDAs without ϵ moves and with bounded stack operation as powerful as PDAs with them?

It is known that PDAs without $\epsilon$ moves are as powerful as PDAs with them. However, it seems to me that the proof allows several stack operations in one move. What happens if we allow at most ...

1
2 3 4 5
8