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We consider the value 1 problem for probabilistic automata over finite words: it asks whether a given probabilistic automaton accepts words with probability arbitrarily close to 1. This problem is known to be undecidable. However, different…
The states of a deterministic finite automaton A can be identified with collections of words in Pf(L(A)) -- the set of prefixes of words belonging to the regular language accepted by A. But words can be ordered and among the many possible…
We present an efficient algorithm to reduce the size of nondeterministic tree automata, while retaining their language. It is based on new transition pruning techniques, and quotienting of the state space w.r.t. suitable equivalences. It…
In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…
An automaton is synchronizing if there is a word that maps all states onto the same state. \v{C}ern\'{y}'s conjecture on the length of the shortest such word is probably the most famous open problem in automata theory. We consider the…
State minimization is a fundamental problem in automata theory. The problem is also of great importance in the study of fuzzy automata. However, most work in the literature considered only state reduction of fuzzy automata, whereas the…
We define a quantum computational model over infinite words, called Measure-Many Quantum B\"uchi Automata (MMQBA), which extends Measure-many Quantum Finite automata (MMQFA) to the infinite word setting with B\"uchi acceptance condition. In…
We study the problem of determinizing $\omega$-automata whose acceptance condition is defined on the transitions using Boolean formulas, also known as transition-based Emerson-Lei automata (TELA). The standard approach to determinize TELA…
We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
Many preference elicitation algorithms consider preference over propositional logic formulas or items with different attributes. In sequential decision making, a user's preference can be a preorder over possible outcomes, each of which is a…
We obtain upper bounds on the number of finite sets $\mathcal S$ of primes below a given bound for which various $2$ variable $\mathcal S$-unit equations have a solution.
In this paper, we investigate the halting problem for deterministic cellula automata in the pentagrid. We prove that the problem is decidable when the cellular automaton starts its computation from a finite configuration and when it has at…
Markov automata combine continuous time, probabilistic transitions, and nondeterminism in a single model. They represent an important and powerful way to model a wide range of complex real-life systems. However, such models tend to be large…
We consider the computability and complexity of decision questions for Probabilistic Finite Automata (PFA) with sub-exponential ambiguity. We show that the emptiness problem for strict and non-strict cut-points of polynomially ambiguous…
Our understanding of the Universe breaks down for very small spacetime intervals, corresponding to an extremely high level of granularity (and energy), commonly referred to as the ``Planck scale''. At this fundamental level, there are…
This paper provides a description of the algorithms employed by the Warwick AUTOMATA package for calculating the finite state automata associated with a short-lex automatic group. The aim is to provide an overview of the whole process,…
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…
This paper tackles the problem of the existence of solutions for recursive systems of Horn clauses with second-order variables interpreted as integer relations, and harnessed by quantifier-free difference bounds arithmetic. We start by…
This paper explores the application of Hurlbert's Linear Optimization Technique to determine bounds on pebbling numbers. By applying Hurlbert's weight functions and optimization methods, we derive upper bounds for specific graph families.…