Related papers: On Complementation of Nondeterministic Finite Auto…
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…
We introduce a measure called width, quantifying the amount of nondeterminism in automata. Width generalises the notion of good-for-games (GFG) automata, that correspond to NFAs of width 1, and where an accepting run can be built on-the-fly…
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…
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…
Nonuniform Deterministic Finite Automata (NUDFA) over monoids were invented by Barrington to study boundaries of nonuniform constant-memory computation. Later, results on these automata helped to indentify interesting classes of groups for…
In this work, we introduce DeepDFA, a novel approach to identifying Deterministic Finite Automata (DFAs) from traces, harnessing a differentiable yet discrete model. Inspired by both the probabilistic relaxation of DFAs and Recurrent Neural…
Affine finite automata (AfA) can be more succinct than probabilistic and quantum finite automata when recognizing some regular languages with bounded-error. In this paper, we improve previously known constructions given for the succinctness…
An acyclic deterministic finite automaton (ADFA) is a data structure that represents a set of strings (i.e., a dictionary) and facilitates a pattern searching problem of determining whether a given pattern string is present in the…
We present an algorithm for regular expression parsing and submatch extraction based on tagged deterministic finite automata. The algorithm works with different disambiguation policies. We give detailed pseudocode for the algorithm,…
We follow a connection between tight determinisation and complementation and establish a complementation procedure from parity automata to nondeterministic B\"uchi automata and prove it to be tight up to an $O(n)$ factor, where $n$ is the…
An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…
Determinisation and completion of finite tree automata are important operations with applications in program analysis and verification. However, the complexity of the classical procedures for determinisation and completion is high. They are…
Deterministic and nondeterministic finite automata (DFAs and NFAs) are abstract models of computation commonly taught in introductory computing theory courses. These models have important applications (such as fast regular expression…
We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it…
The work presents some new algorithms realized recently in the package TESTAS. They decide whether or not deterministic finite automaton (DFA) is synchronizing, several procedures find relatively short synchronizing words and a…
The rapid growth of symbolic data in areas like internet, biological, and financial data has increased the demand for efficient pattern matching and regular expression processing. Non-deterministic Finite Automata (NFA) are used for these…
We construct a probabilistic finite automaton (PFA) with 7 states and an input alphabet of 5 symbols for which the PFA Emptiness Problem is undecidable. The only input for the decision problem is the starting distribution. For the proof, we…
We introduce the category of dependency automata. A dependency automaton consists of two nondeterministic finite automata, with a relation between their states satisfying conditions. This category is equivalent to deterministic finite…
It is proved that every regular expression of alphabetic width $n$, that is, with $n$ occurrences of symbols of the alphabet, can be transformed into a deterministic finite automaton (DFA) with $2^{\frac{n}{2}+(\frac{\log_2…
Complementation of nondeterministic B\"uchi automata (BAs) is an important problem in automata theory with numerous applications in formal verification, such as termination analysis of programs, model checking, or in decision procedures of…