Questions tagged [automata-theory]

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

4
votes
1answer
717 views

Minimal context-free grammar for a regular language

Are there any algorithms for solving exactly the following question? Given a regular language L, represented as a finite automaton say, what is a CFG with minimal number of nonterminals that generates ...
3
votes
0answers
231 views

Providence of pumping lemmas for regular languages

I'm looking to track down who discovered the following pumping lemmas for regular languages. (where $p$ is the pumping constant.) Reg($L) \rightarrow \exists p\forall w(\in L) \forall u_1u_2v(\in \...
6
votes
3answers
415 views

Simplification of weighted NFA

What options does one have for the simplification (meaning reduction in the number of states) of weighted NFA over the probability semiring? From my understanding one can determinize, and then ...
2
votes
1answer
97 views

Are Reversal-bounded Multicounter Machines closed under reversal?

This is a problem I have found very difficult to solve, given how the two different uses of "reversal" confuses search engines. Reversal-bounded multicounter machines are described at length in his ...
12
votes
1answer
330 views

Is there a book/survey-paper outlining language class hierarchies, closure properties, etc

I'm currently doing some Formal Language research involving classes of languages above Regular but below Context Free. I'm looking at things like Reversal-Bounded Multicounter Machines, Single-stack ...
6
votes
3answers
401 views

Chomsky hierarchy for tree structures

I know of the Chomsky hierarchy, which concerns the expressive power of grammars to recognize languages $L \subseteq \Sigma^*$ made of words on an alphabet $\Sigma$. Is there a similar hierarchy for ...
2
votes
1answer
298 views

Number of accepting path of a non deterministic automaton

I have a question that seems to me really natural and have probably already been studied. But keyword search on this site or google does not seems to help me to find any relevent paper. I have got a ...
-1
votes
1answer
100 views

Constructing automata with the same traces, but where a CTL-formula is not equally satisfied [closed]

Hard to put this question in a short title. As part of a self-exercise, I'm trying to solve 6.15b of Principles of Model Checking by Baier and Katoen. You're supposed to prove that there does not ...
7
votes
1answer
216 views

Complete problems and universal simulator machines

I'm trying to get straight in my mind the relation between complete problems and universal simulator machines. Some notions of computability have universal machines (Turing-computability) and some ...
3
votes
1answer
287 views

Deterministic Büchi + its complement covers LTL?

It is well known that deterministic Büchi automata (DBA) are less expressive than non-deterministic Büchi automata (NBA), and in particular DBA are not enough to cover linear temporal logic (LTL). ...
3
votes
0answers
304 views

Name this digraph

I am trying to track down the name of this digraph and some references: You take all members of the transformation semigroup on $n$ elements, $T_{n}$. For two members $x$ ,$y$ ; if $x$ is in the ...
2
votes
0answers
775 views

What is the relationship between the number of states in Quantum Finite Automata and the number of non-regular languages they can recognize?

It is has been shown that Quantum Finite Automata can recognize at least some non-regular languages. What is the relationship between the number of states in a qfa and the number of non-regular ...
7
votes
1answer
324 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^\...
7
votes
0answers
149 views

Size complexity of probabilistic two-way automata for a Boolean function

I'm interested in computing Boolean functions $f:\{0,1\}^n\rightarrow\{0,1\}$ with two-way finite automata and I will measure the complexity of a Boolean function by the number of states for the ...
4
votes
2answers
866 views

Finite state transducer that sorts

Is it possible to sort a string of arbitrary length with a finite-state transducer? How big would this transducer be (the smaller the better)? (I'm not a computer scientist, so less technical answers ...
1
vote
2answers
329 views

Find minimum number of transformations to transform from input to target string

Given that I have an input string, for example: aab And I am given a target string, for example: bababa And then I am given a ...
9
votes
1answer
334 views

Multi-language DFA minimisation

I'm interested in a slight generalisation of DFA. As usual we have state-set $Q$, finite alphabet $\Sigma$, a $\Sigma^*$-action defined on $Q$ by $\delta : Q\times\Sigma\rightarrow Q$, and initial ...
-1
votes
0answers
117 views

How does “δ:Q×Σ→Q” read in the definition of a DFA (deterministic finite acceptor)? [closed]

How do you say "δ:Q×Σ→Q" in English? Describing what "×" and "→" mean would also help.
1
vote
1answer
385 views

How to show that ECTL* is more expressive than CTL* $\cup$ Büchi (with an example)

I am looking for a preferably simple property that is expressible in ECTL* but not in CTL* and not in Büchi, with a citable reference to the proof. Details of what I've tried: I've tried a ...
2
votes
2answers
234 views

Alternating automata

In the paper Fast LTL to Buchi Automata Translation (2001, Gastin and Oddoux) the authors, while defining co-Buchi alternating automata define $\Sigma’= 2^\Sigma$ where $\Sigma$ is the alphabet. ...
4
votes
2answers
301 views

Inductive definition of ECTL*: how are recursive formulas forbidden?

In [1], the extended computation tree logic ECTL* is inductively defined as the propositional formulas over all E($A(F_1,..F_n)$), where E is the existential path quantifier and $A$ some Büchi ...
4
votes
1answer
404 views

Probabilistic circuit complexity or size of probabilistic 2-way automata for Boolean functions

If we consider circuits with arbitrary binary logic gates one can prove by a counting argument that there exists a Boolean function on $n$ variables that require a circuit of size $ \Theta \left( 2^n/...
12
votes
1answer
706 views

The Cost of an Equivalence Query for DFA

Inspired by this question, I am curious about the following: What is the worst-case complexity of checking whether a given DFA accepts the same language as a given regular expression? Is this ...
11
votes
1answer
4k views

What algorithms exist for construction a DFA that recognizes the language described by a given regex?

All of my textbooks use the same algorithm for producing a DFA given a regex: First, make an NFA that recognizes the language of the regex, then, using the subset (aka "powerset") construction, ...
0
votes
2answers
172 views

iterations of a $\epsilon$-FSM transducer on a tape as equivalent to a TM computation

A question partly inspired by a recent question[1] on the utility of FSMs: Years ago noticed the following property of FSM transducers with $\epsilon$-transitions (which allow an "empty" transition ...
5
votes
2answers
2k views

Why were Finite Automata and Turing Machines created?

It seems the creation of Turing Machines and finite automata were apart by at least 2+ decades. That is TMs don't really reference FAs for their working and vice versa; TMs and FAs were developed ...
244
votes
11answers
95k views

What is the enlightenment I'm supposed to attain after studying finite automata?

I've been revising Theory of Computation for fun and this question has been nagging me for a while (funny never thought of it when I learnt Automata Theory in my undergrad). So "why" exactly do we ...
12
votes
2answers
420 views

Why is the state of a FSM traditionally denoted $q$?

While teaching how to implement FSMs using synchronous logical circuits, I noticed an intriguing coincidence: in both the theoretical CS world, and in the electrical engineering world, "state" is ...
9
votes
0answers
145 views

A language outside the Boolean closure of stochastic languages

Stochastic languages, that is, those accepted by probabilistic automata, are known to not be closed under intersection, union, concatenation, and morphism, even on unary languages. I have two ...
1
vote
0answers
90 views

Automatic structures/functions: Is (Z,+) under a unary representation automatic?

The group $(\mathbb{Z}, +)$ is automatic (ala Khoussainov) when using the "standard" representation in a decimal base. But if I want to use a different representation of Z, encoding my integers with ...
14
votes
3answers
735 views

The significance of state complexity in automata and regular languages?

I'm reading "Concatenation of Regular Languages and Descriptional Complexity" by Galina Jiraskova, 2009 on the state complexity resulting from concatenation of two regular languages ( by Galina ...
12
votes
2answers
499 views

Non-isomorphic minimal non-deterministic finite automata

Can somebody provide an example of two equivalent (recognizing the same language) minimal non-deterministic automata (NFA) which are not isomorphic?
4
votes
1answer
211 views

State transducers for generating permutations

Let a finite alphabet $\Sigma$. Let $\mathcal{Reord_\Sigma}$ be the family of computable partial functions between the strings of this alphabet $r\,:\, \Sigma^*\, \rightarrow \Sigma^*$ with the ...
-3
votes
1answer
685 views

Minimal Turing Machine implementation / Von Neumann UC [closed]

I've written a small python program which implements a Turing Machine with a finite tape. It has a tape, a head, a state register and a set of transfer functions ("the program"). The difference to a ...
0
votes
0answers
77 views

Generalizing a set of positive and negative examples through DFAs [duplicate]

Possible Duplicate: Is finding the minimum regular expression an NP-complete problem? Let $\Sigma$ be an alphabet. Let $P$ and $N$ (the set of positive and negative examples) be two disjoint ...
4
votes
1answer
168 views

Getting an automaton from set of words in and out of a language [duplicate]

Possible Duplicate: Is finding the minimum regular expression an NP-complete problem? Let's suppose that I have an unknown language $\mathcal L$, I know only two (particularly large) sets of ...
0
votes
1answer
156 views

Implicit Non-deterministic Buchi determinization

I am doing implicit Buchi determination for LTL logic in hardware where the combinational logic represents the set of states. But instead of using acceptance states, I am using final state (as in ...
6
votes
0answers
266 views

Language of stack configurations of a pushdown automaton

Consider a pushdown automaton $A$ with stack alphabet $\Gamma$. Let $L$ be the language on $\Gamma$ of the stack configurations encountered during accepting runs of $A$. Is $L$ a context-free language?...
9
votes
0answers
251 views

A super-linear time problem in NL

It is a well-known fact that $ \mathsf{NL} = \cup_{k>0} \mathsf{2NFA[k]} $, where $ \mathsf{2NFA[k]} $ is the class of languages recognized by two-way nondeterministic finite automata with $ k>0 ...
17
votes
2answers
416 views

Unary languages recognized by two-way deterministic counter automata

2dca's (two-way deterministic one-counter automata) (Petersen, 1994) can recognize the following unary language: \begin{equation} \mathtt{POWER} = \lbrace 0^{2^n} \mid n \geq 0 \rbrace. \end{...
12
votes
2answers
697 views

Expressiveness of Büchi vs CTL(*)

What is the relationship between the expressiveness of LTL, Büchi/QPTL, CTL and CTL*? Can you give some references that cover as many of these temporal logics as possible (especially between linear- ...
14
votes
2answers
643 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 ...
12
votes
2answers
312 views

Can multipebble automata decide all deterministic context-sensitive languages?

A MPA (multipebble automaton) is a 2DFA (two-way deterministic finite automaton) that can use arbitrary number of pebbles (actually at most $ |w|+2 $ pebbles on a given input $ w $ - the input is ...
3
votes
1answer
200 views

Automatically creating weighted DFAs penalizing sequences of subsets of the alphabet

For a given finite alphabet $\Sigma$, my goal is to write an algorithm that receives as input a sequence $V=V_{1}V_{2}\dots V_{n}$ of subsets ($V_{i}\subseteq\Sigma$), and returns a weighted ...
7
votes
0answers
327 views

Examples of non-CSLs not created through diagonalization

Hopcroft & Ullman 1979, Intro to Automata Theory, Languages, & Computation states (p. 224) that "almost any language one can think of is CSL; the only known proofs that certain languages are ...
14
votes
0answers
202 views

The best known upper bound for two-way probabilistic finite automata with one-counter

It is known that the class of languages recognized by two-way deterministic finite automata with one-counter (2D1CAs) is a proper subset of $ \mathsf{L} $ (deterministic log-space): A 2D1CA can run at ...
4
votes
0answers
230 views

Intersection between register automata and pushdown automata over infinite alphabet

I'm not an expert in automata theory, this is a reference request. As far as I have understood it is known in the automata comunity that register automata by Kaminski are closed by intersection with ...
8
votes
3answers
766 views

1-way Quantum Finite Automata Example Question

I'm attempting to clarify my understanding in the example presented in Section 2.2 of 1-way Quantum Finite Automata: Strengths Weaknesses and Generalizations (this alternative link may also be useful)....
2
votes
0answers
205 views

Fast weighted intersection algorithm for CFG and FSA with self loops but no other circles?

We all know that arbitrary CFG and FSA can be intersected using the Bar-Hillel Construction, whose time complexity is unfortunately too expensive. On the other hand, there are efficient algorithms ...
17
votes
1answer
2k 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 ...