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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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0answers
47 views

Constructing a Minimal Automata for a Language [closed]

for a Language $L$, I want to construct a minimal automata and furthermore also the regular grammar and also describe the minimal automata as a rewriting system. The language is defined as the ...
3
votes
0answers
66 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
0answers
111 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 ...
2
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0answers
92 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
votes
0answers
46 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
votes
1answer
187 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 ...
8
votes
1answer
134 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 ...
3
votes
2answers
141 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, ...
2
votes
1answer
120 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 ...
2
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1answer
96 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 ...
9
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3answers
372 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 ...
10
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2answers
240 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 ...
4
votes
1answer
112 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 $f, g \in \mathbb{F}_q[[z]]$ ...
9
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0answers
88 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 ...
7
votes
2answers
346 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 ...
1
vote
0answers
39 views

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 ...
13
votes
2answers
631 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\...
4
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0answers
69 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.
9
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0answers
120 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 ...
2
votes
1answer
82 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 ...
2
votes
0answers
73 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 ...
1
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0answers
56 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 $\mathcal N := \mathbb N \cup \{\infty\}$ ...
3
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1answer
129 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 $\...
3
votes
3answers
106 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
votes
1answer
125 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 $...
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votes
1answer
49 views

Prove that L* is a regular language [closed]

Suppose that L is any language , not necessarily regular, whose alphabet is {0}; that is the strings of L consist of 0's only. Prove that L* is regular.
5
votes
1answer
105 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 ...
2
votes
1answer
230 views

Existence of an algorithm

I need to show that there exists a polynomial time algorithm that inputs a deterministic automata $A$, and decides if $A$ accepts a word w if and only if it also accepts any word obtained by permuting ...
7
votes
1answer
181 views

Finding a minimal DFA whose language has a desired intersection with another

Suppose I have regular languages $B \subseteq A$, with corresponding (known) minimal deterministic finite automata $M_A, M_B$. I would like to find another regular language $C$ such that $B = A \cap ...
-1
votes
1answer
42 views

Push Down Automata [closed]

Can we put more than one element in stack at a time. Actually I am asking that this transition function is valid for PDA: ∆(q,a,z)=(q',aaz) Where: q and q' are states a is input symbol z is starting ...
3
votes
0answers
86 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, ...
22
votes
2answers
484 views

Testing whether letters can be scheduled to achieve a word in a regular language

I fix a regular language $L$ on an alphabet $\Sigma$, and I consider the following problem that I call letter scheduling for $L$. Informally, the input gives me $n$ letters and an interval for each ...
4
votes
1answer
248 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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votes
1answer
90 views

When designing a DFA, am I allowed to design two separate Machines and perform an Intersection on them? [closed]

I am trying to design a DFA s.t. The set of strings in x ∈ {0, 1}∗ such that the number of zeros is a multiple of 3 and the number of one's is even. My idea was to create two Machines M1 = (Q1, Σ, δ1,...
13
votes
1answer
696 views

Complexity of the problem of words with fewest distinct letters accepted by a finite automaton

Given a finite (deterministic or nondeterministic, I don't think this has much importance) automaton A and a threshold n, does A accept a word containing at most n distinct letters? (By k different ...
12
votes
1answer
135 views

Regular language that discriminates between two deterministic CFGs

Suppose you are given two deterministic push down automata which recognize languages $A$ and $B$, and wish to determine whether there is a regular language $R$ such that $A \subseteq R$ and $R \cap B =...
7
votes
1answer
131 views

Random Deterministic Automata

I am familiar with the term of random graphs, such as $G(n,p)$- a distribution over simple undirected graphs with $n$ vertices, where each edge appears in a graph w.p. $p$. That is, each graph $G=(V,E)...
1
vote
1answer
104 views

Set of languages that can represent every c. e. languange

Could we find any set of languages $S$, such that it can represent every c. e. languange as it's union, intersection, complement, production(times of element ), and $S\subset X$, where $X\subseteq c.e....
3
votes
1answer
62 views

Can any c.e. language with infinite words be decomposed into infinite CFLs with infinite words?

Suppose $L$ is a computably enumerable language, can it be decompose into infinite CFLs with infinite words ? $$L=\bigcup_{L_i\in CFL }^{\infty}L_i$$ Second question: if it is possible that every $L$...
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votes
1answer
74 views

Is there an inherently ambiguous language which can not be recognized by Deterministic LBA?

Is there inherently ambiguous language which can not be recognized by Deterministic LBA? For example, $L=\{wv: w,v=(x|y)^*, w=w^R,v=v^R\}$, is there any deterministc LBA that recognizes $L$ ?
1
vote
0answers
456 views

Equality Constraints over Sets with Tree Automata

Tree Automata can be used to model sets of values of a Herbrand Universe, for example, to model possible values in a functional program. Systems of subtype constraints over set expressions have ...
5
votes
1answer
183 views

What is the motivation behind defining Deterministic Looping Automata?

I was wondering about what could possibly be the motivation behind defining the deterministic looping automata? What puzzles me is that they accept a word iff they have a run on it! I believe they ...
2
votes
1answer
214 views

Deformation of finite regular languages [closed]

Let $L \subseteq \{0,1\}^n$ be any finite regular language s.t it has an acyclic DFA. Let $C$ be some class of acyclic DFAs. Let $\sigma \in S_n$ be a permutation on $n$ symbols. We can apply $\...
4
votes
1answer
1k views

Is Hartmanis-Stearns conjecture settled by this article?

The paper "On the computational complexity of algebraic numbers: the Hartmanis--Stearns problem revisited" by Boris Adamczewski, Julien Cassaigne, Marion Le Gonidec https://arxiv.org/abs/1601....
9
votes
3answers
262 views

Class of languages recognizable by single-tape 3-state TMs

I have for a while been curious about Turing Machines with exactly one tape and exactly 3 states (namely the start state $q_0$, the accept state $q_{accept}$, and the reject state $q_{reject}$). Note ...
1
vote
0answers
74 views

Relation between MDPs and non-deterministic finite automatons

I'm confused as to the relation (computability-wise) between markov decision processes and NFAs. Are finite state MDPs expressible as regular grammars? If so, are markov decision processes thus ...
1
vote
0answers
99 views

Convenient forms of Turing machines

Let us suppose that I have defined a new convenient form of the Turing machine for processing of some specific sort of commonly used structures. This form of TM contains some specific features ...
6
votes
1answer
420 views

Pumping Lemma over 2 way Automaton

Pumping Lemma essentially implies that for a NFA $N$ having $N_0$ states over a unary language $L_0$ any string belonging to $L_0$ can be obtained by 'pumping' one of the strings that have a length ...
6
votes
1answer
222 views

Has there been a study of circuits operating on arrays?

Much ink has been spilled studying the theory surrounding computation by combinatorial circuits operating on bits or boolean values - with AND, OR and NOT gates (as those are enough to implement any ...
9
votes
1answer
222 views

Transition monoid membership for DFAs

Given a complete DFA $A=(Q, \Gamma, \delta, F)$, we can define a collection of functions $f_a$ for each $a\in \Gamma$and with $f_a:Q\rightarrow Q$, $f_a(q)=\delta(q, a)$. We can generalize this notion ...