Related papers: Bounds on the Automata Size for Presburger Arithme…
We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with…
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…
This paper identifies exact probabilistic simulation cost as the natural quantitative measure of quantum advantage for finite automata under strict cutpoints. It gives sharp simulation laws for two representative models. A one-way finite…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages $L$ that assign to each word $w$ a real number $L(w)$. In the case of infinite words, the value of a run is…
We propose several heuristics for mitigating one of the main causes of combinatorial explosion in rank-based complementation of B\"{u}chi automata (BAs): unnecessarily high bounds on the ranks of states. First, we identify elevator…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages~$L$ that assign to each word~$w$ a real number~$L(w)$. In the case of infinite words, the value of a run is…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
In this paper, we investigate the expressive power and the algorithmic properties of weighted expressions, which define functions from finite words to integers. First, we consider a slight extension of an expression formalism, introduced by…
We consider expansions of Presburger arithmetic with families of monadic polynomial predicates. (Examples of such predicates are the set of perfect squares, or the set of integers of the form $2n^3-5n+3$, etc.) Although the full attendant…
This paper studies two issues related to the paper on Computing by Self-reproduction: Autopoietic Automata by Jiri Wiedermann. It is shown that all results presented there extend to deterministic computations. In particular, nondeterminism…
Word equations are a crucial element in the theoretical foundation of constraint solving over strings. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant…
In this note, we present an infinite family of promise problems which can be solved exactly by just tuning transition amplitudes of a two-state quantum finite automata operating in realtime mode, whereas the size of the corresponding…
Subzero automata is a class of tree automata whose acceptance condition can express probabilistic constraints. Our main result is that the problem of determining if a subzero automaton accepts some regular tree is decidable.
Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties. For a well-studied and wide class of…
During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of…
We use an old elementary arithmetic argument to find new upper and lower bounds for Sylvester's denumerant function. These bounds are tight enough to get the asymptotic behavior of the denumerant.
We present a new angle on solving quantified linear integer arithmetic based on combining the automata-based approach, where numbers are understood as bitvectors, with ideas from (nowadays prevalent) algebraic approaches, which work…
Given a nondeterministic finite-state automaton (NFA), we aim to estimate the size of an equivalent deterministic finite-state automaton (DFA). We demonstrate that computing the state complexity of an NFA within polynomial precision is…
We show that a special case of the Feferman-Vaught composition theorem gives rise to a natural notion of automata for finite words over an infinite alphabet, with good closure and decidability properties, as well as several logical…