Questions tagged [automata-theory]

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

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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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Why exactly can real valued time sequences be replaced with rational valued timed sequences?

for my bachelor's thesis I'm looking into timed automata, so I started with A theory of timed automata. On page 16 of the pdf the following proof is provided to show that rationals can be used in time ...
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I need solution for assignment which I've to submit today [closed]

I need solutions i don't have time to learn all this in few hours pls help me. All problem is from book peter linz! Peter linz questions
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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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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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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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1answer
47 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
150 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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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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280 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
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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 ...
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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 ...
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1answer
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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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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
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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 ...
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1answer
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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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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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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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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
91 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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1answer
122 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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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 ...
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1answer
166 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
195 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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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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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,...
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247 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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1answer
155 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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2answers
160 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, ...
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1answer
207 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
179 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 ...
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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 ...
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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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1answer
115 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 $f, g \in \mathbb{F}_q[[z]]$ ...
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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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456 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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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 ...
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661 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\...
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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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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
93 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 ...
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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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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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1answer
180 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 $\...
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3answers
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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 ...
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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 $...
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1answer
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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.
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1answer
129 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 ...
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1answer
234 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 ...
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1answer
208 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 ...

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