The synthesis of stochastic finite-state automata is possible using two kinds of components-deterministic finite-state automata and ergodic signal generators. The starting point in such a synthesis methods is a decomposition of stochastic matrix, its representation as a linear form of simple matrices which belong to the class of transition matrices of deterministic automata. New heuristic crite...

We propose to study value automata with filters, a natural generalization of regular cost automata to nondeterminism. Models such as weighted automata and Parikh automata appear naturally as specializations. Results on the expressiveness of this model offer a general understanding of the behavior of the models that arise as special cases. A landscape of such restrictions is drawn.

This paper defines action-labelled quantitative transition systems as a general framework for combining qualitative and quantitative analysis. We define state-metrics as a natural extension of bisimulation from non-quantitative systems to quantitative ones. We then prove that any single state-metric corresponds to a bisimulation and that the greatest state-metric corresponds to bisimilarity. Fu...

The main goal of this paper is to introduce and study fuzzy multiset regular grammar to show that fuzzy multiset finite automata and fuzzy multiset regular grammars are equivalent. We also study fuzzy multiset linear grammars and fuzzy multiset regular grammars in normal form. Furthermore, we show the equivalence of fuzzy multiset regular grammars, fuzzy multiset left linear grammars, fuzzy mul...

In this note, colorings of the plane by finite sequential machines are compared to previously introduced notions of ultimately periodic tilings of the plane. Finite automata with no counter characterize exactly biperiodic tilings. Finite automata with one counter characterize exactly particles — periodic colorings that are ultimately periodic in every direction. Finite automata with two counter...

Esik and Maletti introduced the notion of a proper semiring and proved that some important (classes of) semirings – Noetherian semirings, natural numbers – are proper. Properness matters as the equivalence problem for weighted automata over a semiring which is proper and finitely and effectively presented is decidable. Milius generalised the notion of properness from a semiring to a functor. As...

This paper presents a .nite-state machine to compute the probability of a word appearance when one knows the left syntactic context. We memorize the token number of words in a dictionary and the token number of syntactic categories on .nite-state automata. We compute a word probability with these numbers. If we have not predicted the awaited word, we take into account the .rst letter for a new ...

We consider words indexed by linear orderings. These extend finite, (bi-)infinite words and words on ordinals. We introduce finite automata and rational expressions for these words. We prove that for countable scattered linear orderings, these two notions are equivalent. This result extends Kleene’s theorem.

We examine a class of infinite two-person games on finitely coloured graphs. The main aim is to construct finite memory winning strategies for both players. This problem is motivated by applications to finite automata on infinite trees. A special attention is given to the exact amount of memory needed by the players for their winning strategies. Based on a previous work of Gurevich and Harringt...

Partitions {Lk}k=1 of A + into m pairwise disjoint languages L1, L2, . . . , Lm such that Lk = L + k for k = 1, 2, . . . , m are considered. It is proved that such a closed partition of A+ can separate the words u1, u2, . . . , um ∈ A+ (i.e. each Lk contains exactly one word of the sequence u1, u2, . . . , um) if and only if for each pair i, j of distinct elements in {1, 2, . . . , m}, the word...