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Register automata (RAs) are finite automata extended with a finite set of registers to store and compare data from an infinite domain. We study the concept of synchronizing data words in RAs: does there exist a data word that sends all…

Formal Languages and Automata Theory · Computer Science 2019-06-11 Karin Quaas , Mahsa Shirmohammadi

Finite state automata (FSA) are ubiquitous in computer science. Two of the most important algorithms for FSA processing are the conversion of a non-deterministic finite automaton (NFA) to a deterministic finite automaton (DFA), and then the…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-03-30 Vlad Slavici , Daniel Kunkle , Gene Cooperman , Stephen Linton

This paper establishes a lower bound on the number of states necessary in the worst case to simulate an $n$-state two-way nondeterministic finite automaton (2NFA) by a one-way unambiguous finite automaton (UFA). It is proved that for every…

Formal Languages and Automata Theory · Computer Science 2024-12-10 Semyon Petrov , Alexander Okhotin

We compare pushdown automata (PDAs for short) against other representations. First, we show that there is a family of PDAs over a unary alphabet with $n$ states and $p \geq 2n + 4$ stack symbols that accepts one single long word for which…

Formal Languages and Automata Theory · Computer Science 2017-06-27 Pierre Ganty , Elena Gutiérrez

This paper studies the complexity of operations on finite automata and the complexity of their decision problems when the alphabet is unary. Let $n$ denote the maximum of the number of states of the input finite automata considered in the…

Formal Languages and Automata Theory · Computer Science 2024-12-16 Wojciech Czerwiński , Maciej Dębski , Tomasz Gogasz , Gordon Hoi , Sanjay Jain , Michał Skrzypczak , Frank Stephan , Christopher Tan

Consider the finite regular language L_n = {w0 : w \in {0,1}^*, |w| \le n}. It was shown by Ambainis, Nayak, Ta-Shma and Vazirani that while this language is accepted by a deterministic finite automaton of size O(n), any one-way quantum…

Quantum Physics · Physics 2007-05-23 Ashwin Nayak

In a recent article by Chapuy and Perarnau, it was shown that a uniformly chosen automaton on $n$ states with a $2$-letter alphabet has a synchronizing word of length $O(\sqrt{n}\log n)$ with high probability. In this note, we improve this…

Combinatorics · Mathematics 2023-07-26 Anders Martinsson

It is shown that, for every $n \geqslant 2$, the maximum length of the shortest string accepted by an $n$-state direction-determinate two-way finite automaton is exactly $\binom{n}{\lfloor\frac{n}{2}\rfloor}-1$ (direction-determinate…

Formal Languages and Automata Theory · Computer Science 2022-10-04 Olga Martynova , Alexander Okhotin

The state complexity of a Deterministic Finite-state automaton (DFA) is the number of states in its minimal equivalent DFA. We study the state complexity of random $n$-state DFAs over a $k$-symbol alphabet, drawn uniformly from the set…

Probability · Mathematics 2013-07-03 Daniel Berend , Aryeh Kontorovich

In this paper, we present a proof of the NP-completeness of computing the smallest Deterministic Finite Automaton (DFA) that distinguishes two given regular languages as DFAs. A distinguishing DFA is an automaton that recognizes a language…

Formal Languages and Automata Theory · Computer Science 2023-06-07 Jan Martens

We study the learnability of symbolic finite state automata (SFA), a model shown useful in many applications in software verification. The state-of-the-art literature on this topic follows the query learning paradigm, and so far all…

Logic in Computer Science · Computer Science 2024-02-14 Dana Fisman , Hadar Frenkel , Sandra Zilles

We investigate the state size of DFAs accepting the shuffle of two words. We provide words u and v, such that the minimal DFA for u shuffled with v requires an exponential number of states. We also show some conditions for the words u and v…

Formal Languages and Automata Theory · Computer Science 2009-07-30 Franziska Biegler , Mark Daley , Ian McQuillan

We introduce a new complexity measure for finite strings using probabilistic finite-state automata (PFAs), in the same spirit as existing notions employing DFAs and NFAs, and explore its properties. The PFA complexity $A_P(x)$ is the least…

Formal Languages and Automata Theory · Computer Science 2024-06-04 Kenneth Gill

Sorting is a fundamental algorithmic pre-processing technique which often allows to represent data more compactly and, at the same time, speeds up search queries on it. In this paper, we focus on the well-studied problem of sorting and…

Data Structures and Algorithms · Computer Science 2023-04-24 Sung-Hwan Kim , Francisco Olivares , Nicola Prezza

Partially ordered nondeterminsitic finite automata (poNFAs) are NFAs whose transition relation induces a partial order on states, that is, for which cycles occur only in the form of self-loops on a single state. A poNFA is universal if it…

Formal Languages and Automata Theory · Computer Science 2017-11-15 Markus Krötzsch , Tomáš Masopust , Michaël Thomazo

The number of states and stack symbols needed to determinize nondeterministic input-driven pushdown automata (NIDPDA) working over a fixed alphabet is determined precisely. It is proved that in the worst case exactly 2^{n^2} states are…

Formal Languages and Automata Theory · Computer Science 2024-04-17 Olga Martynova

We present a strongly exponential lower bound that applies both to the subset synchronization threshold for binary deterministic automata and to the careful synchronization threshold for binary partial automata. In the later form, the…

Formal Languages and Automata Theory · Computer Science 2016-02-16 Vojtěch Vorel

We prove that, paying a polynomial increase in size only, every unrestricted two-way nondeterministic finite automaton (2NFA) can be complemented by a 1-limited automaton (1-LA), a nondeterministic extension of 2NFAs still characterizing…

Formal Languages and Automata Theory · Computer Science 2025-07-16 Bruno Guillon , Luca Prigioniero , Javad Taheri

In this paper we describe an approach to finding the shortest reset word of a finite synchronizing automaton by using a SAT solver. We use this approach to perform an experimental study of the length of the shortest reset word of a finite…

Formal Languages and Automata Theory · Computer Science 2015-03-19 Evgeny Skvortsov , Evgeny Tipikin

We generalize the concept of synchronizing words for finite automata, which map all states of the automata to the same state, to deterministic visibly push-down automata. Here, a synchronizing word w does not only map all states to the same…

Formal Languages and Automata Theory · Computer Science 2020-07-20 Henning Fernau , Petra Wolf