Related papers: Reasoning about Regular Properties: A Comparative …
Even the fastest SMT solvers have performance problems with regular expressions from real programs. Because these performance issues often arise from the problem representation (e.g. non-deterministic finite automata get determinized and…
The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved…
We introduce Symbolic Alternating Finite Automata (s-AFA) as an expressive, succinct, and decidable model for describing sets of finite sequences over arbitrary alphabets. Boolean operations over s-AFAs have linear complexity, which is in…
String analysis is the problem of reasoning about how strings are manipulated by a program. It has numerous applications including automatic detection of cross-site scripting (XSS). A popular string analysis technique includes symbolic…
Constraints over finite sequences of variables are ubiquitous in sequencing and timetabling. Moreover, the wide variety of such constraints in practical applications led to general modelling techniques and generic propagation algorithms,…
Language models (LMs) are often expected to generate strings in some formal language; for example, structured data, API calls, or code snippets. Although LMs can be tuned to improve their adherence to formal syntax, this does not guarantee…
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…
Speculative data-parallel algorithms for language recognition have been widely experimented for various types of finite-state automata (FA), deterministic (DFA) and nondeterministic (NFA), often derived from regular expressions (RE). Such…
We present an efficient algorithm for checking language equivalence of states in top-down deterministic finite tree automata (DFTAs). Unlike string automata, tree automata operate over hierarchical structures, posing unique challenges for…
Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware. The main advantage of the alternating model of computation is that complementation is…
Given an order of the underlying alphabet we can lift it to the states of a finite deterministic automaton: to compare states we use the order of the strings reaching them. When the order on strings is the co-lexicographic one \emph{and}…
We introduce first order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first order formulae, with states and internal variables given by uninterpreted…
This paper deals with model checking problems with respect to LTL properties under fairness assumptions. We first present an efficient algorithm to deal with a fragment of fairness assumptions and then extend the algorithm to handle…
In automata theory, while determinisation provides a standard route to solving many common problems in automata theory, some weak forms of nondeterminism can be dealt with in some problems without costly determinisation. For example, the…
In the present work, we lay out a new theory showing that all automata can always be co-lexicographically partially ordered, and an intrinsic measure of their complexity can be defined and effectively determined, namely, the minimum width…
We present new results on realtime alternating, private alternating, and quantum alternating automaton models. Firstly, we show that the emptiness problem for alternating one-counter automata on unary alphabets is undecidable. Then, we…
In coding and information theory, it is desirable to construct maximal codes that can be either variable length codes or error control codes of fixed length. However deciding code maximality boils down to deciding whether a given NFA is…
In a recent paper we analyzed the space complexity of streaming algorithms whose goal is to decide membership of a sliding window to a fixed language. For the class of regular languages we proved a space trichotomy theorem: for every…
Large language models (LLMs) have demonstrated strong performance on formal language tasks, yet whether this reflects genuine symbolic reasoning or pattern matching on familiar constructions remains unclear. We introduce a benchmark for…
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,…