16 research outputs found
Crisp-determinization of weighted tree automata over strong bimonoids
We consider weighted tree automata (wta) over strong bimonoids and their
initial algebra semantics and their run semantics. There are wta for which
these semantics are different; however, for bottom-up deterministic wta and for
wta over semirings, the difference vanishes. A wta is crisp-deterministic if it
is bottom-up deterministic and each transition is weighted by one of the unit
elements of the strong bimonoid. We prove that the class of weighted tree
languages recognized by crisp-deterministic wta is the same as the class of
recognizable step mappings. Moreover, we investigate the following two
crisp-determinization problems: for a given wta , (a) does there
exist a crisp-deterministic wta which computes the initial algebra semantics of
and (b) does there exist a crisp-deterministic wta which computes
the run semantics of ? We show that the finiteness of the Nerode
algebra of implies a positive answer for (a),
and that the finite order property of implies a positive answer for
(b). We show a sufficient condition which guarantees the finiteness of and a sufficient condition which guarantees the finite order
property of . Also, we provide an algorithm for the construction of
the crisp-deterministic wta according to (a) if is finite,
and similarly for (b) if has finite order property. We prove that it
is undecidable whether an arbitrary wta is crisp-determinizable. We
also prove that both, the finiteness of and the finite
order property of are undecidable
Weighted Tree Automata -- May it be a little more?
This is a book on weighted tree automata. We present the basic definitions
and some of the important results in a coherent form with full proofs. The
concept of weighted tree automata is part of Automata Theory and it touches the
area of Universal Algebra. It originated from two sources: weighted string
automata and finite-state tree automata
Weighted Finite Automata over Strong Bimonoids
We investigate weighted finite automata over strings and strong bimonoids. Such algebraic structures satisfy the same laws as semirings except that no distributivity laws need to hold. We define two different behaviors and prove precise characterizations for them if the underlying strong bimonoid satisfies local finiteness conditions. Moreover, we show that in this case the given weighted automata can be determinized
Weighted Automata over Vector Spaces
In this paper we deal with three models of weighted automata that take
weights in the field of real numbers. The first of these models are classical
weighted finite automata, the second one are crisp-deterministic weighted
automata, and the third one are weighted automata over a vector space. We
explore the interrelationships between weighted automata over a vector space
and other two models.Comment: In Proceedings AFL 2023, arXiv:2309.0112
Weighted automata and multi-valued logics over arbitrary bounded lattices
AbstractWe show that L-weighted automata, L-rational series, and L-valued monadic second order logic have the same expressive power, for any bounded lattice L and for finite and infinite words. We also prove that aperiodicity, star-freeness, and L-valued first-order and LTL-definability coincide. This extends classical results of Kleene, Büchi–Elgot–Trakhtenbrot, and others to arbitrary bounded lattices, without any distributivity assumption that is fundamental in the theory of weighted automata over semirings. In fact, we obtain these results for large classes of strong bimonoids which properly contain all bounded lattices