Questions tagged [automata-theory]

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

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Design a NFA and DFA which accepts: (1+01)*(0+00)(1+10)* [closed]

This is the DFA I came up with, but it does not match the answer. I can't find the mistake. Any help will be appreciated
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2answers
251 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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4answers
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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 ...
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2answers
142 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 ...
4
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1answer
163 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
162 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
159 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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56 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
155 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
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42 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
50 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
116 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 ...
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1answer
165 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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1answer
93 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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58 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
72 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
90 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 ...
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59 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
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1answer
73 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 ...
8
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1answer
226 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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97 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
53 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,...
8
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1answer
150 views

A conjecture related to the Cerny conjecture - counterexample/reference request

The Cerny conjecture is the statement that any synchronizing automaton with $n$ states has a synchronizing word of length at most $(n-1)^2$. The best current upper bound for the length of a ...
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0answers
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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 $2 \times 10^6$ ...
3
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2answers
156 views

Compactness of domino tilings

I've read in Lemma 2 of the paper 1 that if every square region of the plane admits a tiling, then the whole plain admits a tiling, but the proof is omitted. This sounds like a compactness property, ...
13
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1answer
455 views

Fast sparse boolean matrix chain product

So, I've got about 100-200 very sparse square boolean matrices with side length ~several dozens, and I need to compute their product. I know that if I multiply them serially, the product will usually ...
13
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2answers
640 views

Automata learning without counterexamples

In Angluin's automata learning framework, a student aims to learn a regular language $L\subseteq \Sigma^*$ by asking two types of questions to his teacher: Word queries: given $w\in \Sigma^*$, is $w\...
9
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3answers
390 views

Continuous mathematics and formal language theory

Whether there are some results on solving formal languages problems using mathematical analysis, continuous mathematics. For example, solving the intersection non-emptiness problem for a context-free ...
7
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3answers
426 views

Where does the modern canonical version of the Turing machine come from?

Turing's original 1936 description of his a-machine differs in several respects from the Turing machine I studied at university, leading me to questions: The Turing machine I learned about was ...
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1answer
146 views

Automata as term rewriting systems

It came to my mind that automata (say to start DFA) can be thought as a special kind of rewriting systems. So if one has a word w , one tries to reduce it to the $\epsilon$ word. In other words ...
11
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2answers
270 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 ...
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5answers
595 views

What notable automaton models have polynomially-decidable containment?

I'm trying to solve a particular problem, and I thought I might be able to solve it using automata theory. I'm wondering, what models of automata have containment decidable in polynomial time? i.e. if ...
4
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1answer
114 views

Applications of Christol theorem

I'm looking forward to know about applications of Christol theorem mentioned in Jefrrey Shallit's Number theory and formal languages. One of them is purely algebraic: if $f, g \in \mathbb{F}_q[[z]]$ ...
3
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1answer
206 views

Finding self-similar homomorphisms of a FSM transducer

Consider a special case of homomorphisms of FSM transducers (or "generalized sequential machines" in [1]). Let $F$ be a transducer accepting a language $L$, and let $h(x)$ be a homomorphism function ...
7
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2answers
426 views

Are all turing machines paths predictable?

I was recently studying partial solutions to the halting problem and came across the problem which I discuss below. In particular I was studying when it was computable to tell if a turing machine has ...
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0answers
100 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 ...
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Question About Turing Machine Computability [closed]

If p is a Turing machine then L(p) = {x | p(x) = yes}. Let A = {p | p is a Turing machine and L(p) is a finite set}. Is A computable? Justify your answer. So I'm trying to figure out how to solve ...
11
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1answer
2k views

Given a PDA M such that L(M) is in DCFL construct a DPDA N such that L(N) = L(M)

Is it possible to construct an algorithm which takes as input a pushdown automaton $M$ along with the promise that the language accepted by this automaton $L(M)$ is a deterministic context-free ...
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0answers
73 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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144 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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1answer
471 views

Number of equivalence classes in regular languages as a function of DFA size

This question is related to a recent question by Janoma. Background In constraint programming, a regular global constraint $c$ over a domain $D$ is a pair $(s, M)$ with $s$ a tuple of variables (...
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1answer
726 views

Eilenberg's rational hierarchy of nonrational automata & languages — where is it now?

In the preface to his very influential books Automata, Languages and Machines (Volumes A, B), Samuel Eilenberg tantalizingly promised Volumes C and D dealing with "a hierarchy (called the rational ...
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1answer
91 views

Can a det. $k$-counter machine ($k \geq 2$) be simulated by a det. $k'$-counter machine using non-$\epsilon$-moves followed by $\epsilon$-moves?

I have a question concerning deterministic $k$-counter machines, for $k \geq 2$. Recall that in this context, the determinism is expressed by the fact that the machine can never face a choice between ...
3
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0answers
83 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 ...
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4answers
3k views

Where do most REGEX implementations fall on the complexity scale?

Most modern implementations of regular expressions, such as the ones in perl or .NET, go beyond the classical computer science definition of REGEXes with features like lookahead and lookbehind. Do ...
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59 views

Rational power series over $\mathbb N \cup \{\infty\}$, rationality of singular part

Let $\Sigma$ be a finite alphabet, and consider the formel power series over $\Sigma$ considered as non-commuting variables with coefficients in the semiring $\mathcal N := \mathbb N \cup \{\infty\}$ ...
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2answers
519 views

How small can a NFA be, compared to the minimal Unambiguous Finite Automaton (UFA) of the same regular language?

Unambiguous Finite Automatons (UFA) are special type of non-deterministic finite automatons (NFA). A NFA is called unambiguous if every word $w\in \Sigma^*$ has at most one accepting path. This ...
3
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3answers
111 views

Example of monoid $M$ such that $\operatorname{RAT}(M) \not\subseteq \operatorname{REC}(M)$

Let $M$ be a monoid, the family of rational sets $\operatorname{RAT}(M)$ is defined as the smallest set containing the finite subsets, and closed under union, concatentaion and the star operation. The ...
9
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1answer
137 views

Generalisation of the statement that a monoid recognizes language iff syntactic monoid divides monoid

Let $A$ be a finite alphabet. For a given language $L \subseteq A^{\ast}$ the syntactic monoid $M(L)$ is a well-known notion in formal language theory. Furthermore, a monoid $M$ recognizes a language $...
3
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1answer
170 views

“Combining” two mealy machines [closed]

How could you combine two mealy machines, the first one $M_1$ has as input $\sum_{1}^*$ and as output $\sum_{2}^*$, the second machine $M_2$ uses the output $\sum_{2}^*$ as the input and outputs $\...