21,081 research outputs found
On Determinism and Unambiguity of Weighted Two-way Automata
In this paper, we first study the conversion of weighted two-way automata to
one-way automata. We show that this conversion preserves the unambiguity but
does not preserve the determinism. Yet, we prove that the conversion of an
unambiguous weighted one-way automaton into a two-way automaton leads to a
deterministic two-way automaton. As a consequence, we prove that unambiguous
weighted two-way automata are equivalent to deterministic weighted two-way
automata in commutative semirings.Comment: In Proceedings AFL 2014, arXiv:1405.527
Root-Weighted Tree Automata and their Applications to Tree Kernels
In this paper, we define a new kind of weighted tree automata where the
weights are only supported by final states. We show that these automata are
sequentializable and we study their closures under classical regular and
algebraic operations. We then use these automata to compute the subtree kernel
of two finite tree languages in an efficient way. Finally, we present some
perspectives involving the root-weighted tree automata
Weighted Automata and Expressions over Pre-Rational Monoids
The Kleene theorem establishes a fundamental link between automata and expressions over the free monoid. Numerous generalisations of this result exist in the literature; on one hand, lifting this result to a weighted setting has been widely studied. On the other hand, beyond the free monoid, different monoids can be considered: for instance, two-way automata, and even tree-walking automata, can be described by expressions using the free inverse monoid. In the present work, we aim at combining both research directions and consider weighted extensions of automata and expressions over a class of monoids that we call pre-rational, generalising both the free inverse monoid and graded monoids. The presence of idempotent elements in these pre-rational monoids leads in the weighted setting to consider infinite sums. To handle such sums, we will have to restrict ourselves to rationally additive semirings. Our main result is thus a generalisation of the Kleene theorem for pre-rational monoids and rationally additive semirings. As a corollary, we obtain a class of expressions equivalent to weighted two-way automata, as well as one for tree-walking automata
A Coalgebraic Approach to Reducing Finitary Automata
Compact representations of automata are important for efficiency. In this
paper, we study methods to compute reduced automata, in which no two states
accept the same language. We do this for finitary automata (FA), an abstract
definition that encompasses probabilistic and weighted automata. Our procedure
makes use of Milius' locally finite fixpoint. We present a reduction algorithm
that instantiates to probabilistic and S-linear weighted automata (WA) for a
large class of semirings. Moreover, we propose a potential connection between
properness of a semiring and our provided reduction algorithm for WAs, paving
the way for future work in connecting the reduction of automata to the
properness of their associated coalgebras
Pebble Weighted Automata and Weighted Logics
34 pagesInternational audienceWe introduce new classes of weighted automata on words. Equipped with pebbles, they go beyond the class of recognizable formal power series: they capture weighted first-order logic enriched with a quantitative version of transitive closure. In contrast to previous work, this calculus allows for unrestricted use of existential and universal quantifications over positions of the input word. We actually consider both two-way and one-way pebble weighted automata. The latter class constrains the head of the automaton to walk left-to-right, resetting it each time a pebble is dropped. Such automata have already been considered in the Boolean setting, in the context of data words. Our main result states that two-way pebble weighted automata, one- way pebble weighted automata, and our weighted logic are expressively equivalent. We also give new logical characterizations of standard recognizable series
Automata and rational expressions
This text is an extended version of the chapter 'Automata and rational
expressions' in the AutoMathA Handbook that will appear soon, published by the
European Science Foundation and edited by JeanEricPin
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