相关论文: Morphisms and minimisation of weighted automata

This chapter is concerned with the design and analysis of algorithms for minimizing finite automata. Getting a minimal automaton is a fundamental issue in the use and implementation of finite automata tools in frameworks like text…

The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…

We consider the state-minimisation problem for weighted and probabilistic automata. We provide a numerically stable polynomial-time minimisation algorithm for weighted automata, with guaranteed bounds on the numerical error when run with…

We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a…

This paper is concerned with the computational complexity of equivalence and minimisation for automata with transition weights in the field Q of rational numbers. We use polynomial identity testing and the Isolation Lemma to obtain…

This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in…

Partition refinement is a method for minimizing automata and transition systems of various types. Recently, we have developed a partition refinement algorithm that is generic in the transition type of the given system and matches the run…

Coalgebraic bisimilarity minimization generalizes classical automaton minimization to a large class of automata whose transition structure is specified by a functor, subsuming strong, weighted, and probabilistic bisimilarity. This offers…

We present an efficient algorithm for computing the partial bisimulation preorder and equivalence for labeled transitions systems. The partial bisimulation preorder lies between simulation and bisimulation, as only a part of the set of…

We present a disambiguation algorithm for weighted automata. The algorithm admits two main stages: a pre-disambiguation stage followed by a transition removal stage. We give a detailed description of the algorithm and the proof of its…

Probabilistic automata constitute a versatile and elegant model for concurrent probabilistic systems. They are equipped with a compositional theory supporting abstraction, enabled by weak probabilistic bisimulation serving as the reference…

In this paper we regard languages and their acceptors -- such as deterministic or weighted automata, transducers, or monoids -- as functors from input categories that specify the type of the languages and of the machines to categories that…

Hyper-minimization is a state reduction technique that allows a finite change in the semantics. The theory for hyper-minimization of deterministic weighted tree automata is provided. The presence of weights slightly complicates the…

Stone-type dualities provide a powerful mathematical framework for studying properties of logical systems. They have recently been fruitfully explored in understanding minimisation of various types of automata. In Bezhanishvili et al.…

We present abstraction-refinement algorithms for model checking safety properties of timed automata. The abstraction domain we consider abstracts away zones by restricting the set of clock constraints that can be used to define them, while…

In this paper we regard languages and their acceptors - such as deterministic or weighted automata, transducers, or monoids - as functors from input categories that specify the type of the languages and of the machines to categories that…

Quotient is a basic operation of formal languages, which plays a key role in the construction of minimal deterministic finite automata (DFA) and the universal automata. In this paper, we extend this operation to formal power series and…

We propose a new method, that we coined the ``morphism-trick'', to integrate custom implementations of vector-Jacobian products in automatic differentiation softwares, applicable to a wide range of semiring-based computations. Our approach…

Partition refinement is a method for minimizing automata and transition systems of various types. Recently, we have developed a partition refinement algorithm that is generic in the transition type of the given system and matches the run…

Abstraction is a commonly used process to represent some low-level system by a more coarse specification with the goal to omit unnecessary details while preserving important aspects. While recent work on abstraction in the situation…