Questions tagged [automata-theory]

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

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1answer
93 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^* ...
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0answers
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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 ...
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1answer
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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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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 ...
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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 ...
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1answer
114 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 ...
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1answer
321 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 $...
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0answers
125 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 ...
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0answers
114 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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4answers
476 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 ...
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1answer
360 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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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?
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2answers
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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
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1answer
156 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 ...
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2answers
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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
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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 ...
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3answers
436 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 ...
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1answer
83 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 ...
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0answers
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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 ...
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5answers
401 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 ...
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0answers
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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 ...
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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 ...
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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 ...
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1answer
51 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 ...
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1answer
158 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 ...
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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 ...
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2answers
763 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
166 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
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1answer
132 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 ...
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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 ...
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1answer
404 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
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2answers
419 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
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1answer
90 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' ...
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2answers
393 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
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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
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1answer
216 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
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1answer
170 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 ...
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1answer
201 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 ...
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0answers
58 views

Information theory for Mathematical Physics [duplicate]

What are some good introductory texts on information theory for someone who is classically trained in mathematical physics? Unfortunately my abilities in computer sciences and formal logic are next ...
10
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1answer
208 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 ...
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0answers
51 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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1answer
56 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
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1answer
130 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 ...
4
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1answer
96 views

Deterministic Realtime Languages

Book and Greibach (V. Book, Ronald & A. Greibach, Sheila. (1970). Quasi-realtime languages. Theory of Computing Systems. 4. 97-111. 10.1007/BF01705890.) prove that non-deterministic linear time ...
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0answers
67 views

Language recongized by a “quasi realtime register machine”?

Counter machines are very powerful. Even two counters suffice for making these Turing complete. But, in simulating a Turing machine the counter machine encodes in its integers a large amount of data. ...
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1answer
81 views

DPDA with parameterized states

I'm considering an extension of Sublime Text's syntax definition format. A syntax definition is, in essence, a specification of a deterministic pushdown automaton. I would like to extend the system to ...
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1answer
94 views

What is the formal definition of a stacked based finite state machine?

The formal definition of a finite state machine is as follows: A FSM is a quintuple: ($I$, $S$, $S$0, $T$, $F$) $I$ - finite, non-empty input set $S$ - finite, non-empty state set $S$0 - initial state ...
3
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1answer
78 views

Agnostic query learning for DFAs

Angluin's membership+equivalence query algorithm allows to efficiently and exactly learn a target $n$-state DFA. But what if the target DFA is huge, or the target concept is not even a regular ...
9
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1answer
265 views

Turing Machines as Coalgebras

I'm looking to write a survey on the method of representing the dynamics of state-based computation within the framework of coalgebras. So far I've managed to find papers on coalgebra representations ...
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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, ...

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