# Questions tagged [automata-theory]

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

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### Equivalence between GNFA and NFA/DFA

In Section 1.3 of the 3rd edition of Michael Sipser’s Introduction to the Theory of Computation, it is proven that regular expressions are equivalent to deterministic finite automatas (DFAs). That is, ...
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### Complexity of the inevitability problem over monoids

I am interested in the complexity of following problem: Inevitability problem in monoids Input: two regular languages $K$, $L$ specified by finite monoids $M_K$ and $M_L$ (+ morphisms and accepting ...
317 views

### Converting 2-ambiguous NFA to unambiguous NFA

This must be known, but somehow I can't locate a reference about this. Let $A$ be a nondeterministic finite automaton (NFA) over words of an alphabet $\Sigma$. I say that $A$ is unambigous if, for ...
1 vote
63 views

### Utility of automated alphabet abstraction in automata learning?

In (active) automata learning, a learner tries to infer an appropriate model for a black-box executable state machine by systematically feeding different inputs into it and observing the corresponding ...
1 vote
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### Real life application of two-way DFA

I am currently studying two-way DFA and I couldn't find and research anything on its real-life applications if there are any. I am very unsure where it could be used and any ideas would be great. tyia
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### Construction of a PDA for the binary and decimal representation of a number

I have the solution with me for this question but I have really hard time understanding the construction. Can anyone may be break it down in a simpler way? Problem: Given $n \in \mathbb{N}^+$. ...
136 views

### Is $a^m b^n$ where $m - n \sqrt{2} \ge 0$ context-free?

Is the language $a^m b^n$ where $m - n \sqrt{2} \ge 0$ a context-free language? I’m suspecting that it’s not, but I haven’t been able to prove so using the pumping lemma for context-free languages. ...
83 views

### Linear-time maze exploration for finite automaton with pebbles?

Blum and Kozen have shown that a robot with the computational capabilities of a finite automaton can visit all $n$ cells in a quadratic maze when the robot is equipped with two pebbles which it may ...
109 views

### What is the Simplest type of automaton that can simulate all DFAs?

During recent research in a somewhat unrelated field (Spin Physics), I stumbled across a subclass of regular languages. The context of the research poses the question what the minimal power of the ...
111 views

### Logical Equivalents of Finite State Transducers

There's a notion of "regular" function on words in automata theory that corresponds nicely to functions in WS1S/Büchi Arithmetic/the logic of words with a prefix and equal-length relation. ...
74 views

### State-based vs. transition-based definitions of alternating automata

Maybe this is a naïve question but I'm having difficulties finding the answer in the literature. Alternating finite automata (AFA) are usually defined in modern literature in the following terms. An ...
62 views

### Number of quantifier alternations in prenex form of a formula

I'm currently studying hyperlogics and in particular HyperLTL/CTL*. In model checking algorithms for such logics the number of quantifier alternations appearing in a formula can play an important role ...
99 views

### The difference between the 1st and 2nd editions. "Compilers Principles, Techniques, and Tools" by Aho, Sethi and Ullman

I bought "Compilers Principles, Techniques, and Tools 1st Edition" by Alfred V. Aho, Ravi Sethi and Jeffrey D. Ullman long years ago and it has been sitting on my bookshelf ever since. I ...
173 views

### Pumping lemma for CFL intersection

The class of context-free languages is not closed under intersection. For example, the language $L=\{a^nb^nc^n : n\geq 0\}$ is not context-free, but it is an intersection of two context-free languages....
5k views

### Theoretical Computer Science vs other Sciences?

So I‘m in my fifth semester studying Computer Science at a German university, so I‘ve only scratched the surface of Theoretical Computer Science, namely Logic, Formal Languages, Automata Theory, ...
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### Equivalent Characterizations of Semilinear Sets

Coming from an automata theory background, the semilinear sets seem like an ideal candidate for having lots of equivalent characterizations. I am already familiar with a few well known ones: Sets ...
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### Relationship between the transition monoid of an automaton and its adjacency matrix

Let $A=(Q,\Sigma, \Delta, q_0, F)$ be an NFA over an alphabet $\Sigma$, $M(A)$ be its transition monoid. For all $a\in\Sigma$, let $S_a\in\mathbb{B}^{|Q|\times|Q|}$ be the adjacency matrix of $A$ ...
144 views

### Arithmetization of finite automata

Is there any standard way to encode the language accepted by a finite automaton by an arithmetic formula? A particular way of doing this would be to extend the language of existential integer linear ...
415 views

### Are regular expressions inherently more difficult to construct than DFAs for humans?

When I am asked to construct a regular expression and DFA that would accept a language $L$, I usually find it much easier to construct the DFA (almost coming mechanically for me) than it is to ...
109 views

### Encoding of finite automata in Intersection Non-Emptiness problem

The intersection non-emptiness problem is defined as follows: Given a list of deterministic finite automata as input, the goal is to determine whether or not their associated regular languages have a ...
1 vote
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### Definition in some old paper about formal power series (automata theory)

I have a question about a term in a paper about formal power series. It was never defined but the author used $K \langle A \rangle$, what set is $K \langle A \rangle$? Here $K$ is a field (commutative ...
46 views

### Applying Angluin's automata learning to build Tree Automata

I have two different questions: a broad question (Q1) and a specific question (Q2). Q1: Is there any established or well-accepted mechanism to learn tree automata based on Angluin's style of learning ...
165 views

### Check whether DFA accepts majority of words less than a cutoff with another DFA

Question Let $M$ be some DFA that reads integers in base $k$. Does there always exist some other DFA $M'$ that also reads integers in base $k$, where $M'(x)$ accepts if and only if $M$ accepts the ...
1 vote
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### What is region construction in timed automata?

I've recently started self-learning timed automata. There's this theorem in there that a timed automaton can be converted to a DFA using a "region" construction. I've looked up references on ...
89 views

### Is there any context-free language that is inherently ambiguous as an indexed language

Indexed languages are defined as being produced by indexed grammar. Is there any context-free language that is inherently ambiguous as an indexed language? That is, is there a context-free language ...
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### Is there any inherently ambiguous indexed language?

Indexed languages are defined as being produced by an indexed grammar. My question is: Is there an indexed language such that there is no indexed grammar that can produce every word of the language in ...
202 views

### Most non-deterministic automaton

My question is about how to construct, given a number n, an NFA with n states which gets converted to a complete (i.e., with no omitted transitions) DFA with exactly $2^n$ reachable states (even ...
286 views

### Existence of injective length-preserving rational function to a smaller alphabet

(This is a simpler rephrasing of an earlier question I have since deleted.) Definitions For this question, a finite-state transducer is like a standard NFA, except at each transition, the transducer ...
132 views

### Characterization of lengths of words accepted by DFAs

Let $M$ be an arbitrary DFA. For each $n \in \mathbb{N}$, let $f_M(n)$ be the number of words of length $n$ accepted by $M$. Then, consider the set of all such $f_M$ for all DFAs $M$. Is there a nice ...
89 views

### What set of sequential 2-bit inputs would it take for any system with 2 bits of memory to not be able to know it is not being tested?

In a computer game, a player is tasked with making a sequential circuit that takes two one-bit inputs (for a total of four combinations) and outputs a bit depending on both the current input and the ...
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### Nondeterministic polynomial time languages with linearly bounded certificates

Define the class $X$ of languages by the condition that a language $L$ over alphabet $\Sigma$ is in $X$ iff there are a constant $c > 0$ and a polynomial-time checking relation $R$ such that for ...
147 views

I have been reading about TSO (total store order) memory models for concurrent programs, but I can not find resources for PSO (partial store order) memory models. Can someone please point to resources....
1 vote
135 views

### Bounded non-emptiness intersection of deterministic context-free grammars

Let A and B be two determinstic context-free grammar, and let N be an integer: What's the complexity of deciding if the intersection of the languages accepted by A and B over all strings of length ...
170 views

### Alternative to LBA for recognising context-sensitive languages

I've always felt that there's no "canonical" automata for recognising context-sensitive languages. Much like there's DFA for regular, PDA for context-free and Turing machines for RE. I'm ...
105 views

### Expressiveness of pushdown automata whose stack height sequence is unambiguous

I consider pushdown automata on an alphabet $\Sigma$, which are intuitively finite automata with a stack. Formally, a pushdown automaton $A = (Q, q_0, F, \Gamma, \Delta)$ is a finite set $Q$ of states,...
445 views

### Complexity of NFA to DFA minimization with binary threshold

What is the complexity of the following problem? Given an NFA $A$ and a number $k\in \mathbb{N}$ in binary encoding, does there exist a DFA $B$ with at most $k$ states such that $L(A)=L(B)$? ...
173 views

### Regular Expressions that converts into unambiguous automata

Brüggemann-Klein and Wood (1992) proved that a certain kind of regular expressions, that they call “Deterministic Regular expressions”, when converted into automata using the Glushkov's Construction, ...