arXiv subjects

Peter Kostolányi

Publications and source records attributed to Peter Kostolányi.

3 recordsLinked to original sources

arXiv2026

Reversible Weighted Automata over Finite Rings and Monoids with Commuting Idempotents

Reversible weighted automata are introduced and considered in a specific setting where the weights are taken from a nontrivial locally finite commutative ring such as a finite field. It is shown that the supports of series realised by such automata are precisely the rational languages such that the idempotents in their syntactic monoids commute. In particular, this is true for reversible weighted automata over the finite field $\mathbb{F}_2$, where the realised series can be directly identified with such languages. A new automata-theoretic characterisation is thus obtained for the variety of rational languages corresponding to the pseudovariety of finite monoids $\mathbf{ECom}$, which also forms the Boolean closure of the reversible languages in the sense of J.-É. Pin. The problem of determining whether a rational series over a locally finite commutative ring can be realised by a reversible weighted automaton is decidable as a consequence.

cs.FL↗

arXiv2024

Weighted Automata and Logics Meet Computational Complexity

Complexity classes such as $\#\mathbf{P}$, $\oplus\mathbf{P}$, $\mathbf{GapP}$, $\mathbf{OptP}$, $\mathbf{NPMV}$, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in terms of a class $\mathbf{NP}[S]$ for a suitable semiring $S$, defined via weighted Turing machines over $S$ similarly as $\mathbf{NP}$ is defined via the classical nondeterministic Turing machines. Other complexity classes of decision problems can be lifted to the quantitative world using the same recipe as well, and the resulting classes relate to the original ones in the same way as weighted automata or logics relate to their unweighted counterparts. The article surveys these too-little-known connexions between weighted automata theory and computational complexity theory implicit in the existing literature, suggests a systematic approach to the study of weighted complexity classes, and presents several new observations strengthening the relation between both fields. In particular, it is proved that a natural extension of the Boolean satisfiability problem to weighted propositional logic is complete for the class $\mathbf{NP}[S]$ when $S$ is a finitely generated semiring. Moreover, a class of semiring-valued functions $\mathbf{FP}[S]$ is introduced for each semiring $S$ as a counterpart to the class $\mathbf{P}$, and the relations between $\mathbf{FP}[S]$ and $\mathbf{NP}[S]$ are considered.

cs.FL↗

arXiv2023

Bideterministic Weighted Automata

A finite automaton is called bideterministic if it is both deterministic and codeterministic -- that is, if it is deterministic and its transpose is deterministic as well. The study of such automata in a weighted setting is initiated. All trim bideterministic weighted automata over integral domains and over positive semirings are proved to be minimal. On the contrary, it is observed that this property does not hold over commutative rings in general: non-minimal trim bideterministic weighted automata do exist over all semirings that are not zero-divisor free, and over many such semirings, these automata might not even admit equivalents that are both minimal and bideterministic. The problem of determining whether a given rational series is realised by a bideterministic automaton is shown to be decidable over fields and over tropical semirings. An example of a positive semiring over which this problem becomes undecidable is given as well.

cs.FL↗