Quasi-Distances and Weighted Finite Automata
نویسندگان
چکیده
We show that the neighbourhood of a regular language L with respect to an additive quasi-distance can be recognized by an additive weighted finite automaton (WFA). The size of the WFA is the same as the size of an NFA (nondeterministic finite automaton) for L and the construction gives an upper bound for the state complexity of a neighbourhood of a regular language with respect to a quasi-distance. We give a tight lower bound construction for the determinization of an additive WFA using an alphabet of size five. The previously known lower bound construction needed an alphabet that is linear in the number of states of the WFA.
منابع مشابه
Reduction of Computational Complexity in Finite State Automata Explosion of Networked System Diagnosis (RESEARCH NOTE)
This research puts forward rough finite state automata which have been represented by two variants of BDD called ROBDD and ZBDD. The proposed structures have been used in networked system diagnosis and can overcome cominatorial explosion. In implementation the CUDD - Colorado University Decision Diagrams package is used. A mathematical proof for claimed complexity are provided which shows ZBDD ...
متن کاملOn Finite and Polynomial Ambiguity of Weighted Tree Automata
We consider finite and polynomial ambiguity of weighted tree automata. Concerning finite ambiguity, we show that a finitely ambiguous weighted tree automaton can be decomposed into a sum of unambiguous automata. For polynomial ambiguity, we show how to decompose a polynomially ambiguous weighted tree automaton into simpler polynomially ambiguous automata and then analyze the structure of these ...
متن کاملComplementation and Inclusion of Weighted Automata on Infinite Trees
Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this report we study the problems of intersection, complementation and inclusion for weighted automata on infinite trees and show that they are not harder than reasoning w...
متن کاملThe Inclusion Problem for Weighted Automata on Infinite Trees
Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this paper we study the problems of intersection, complementation and inclusion for weighted automata on infinite trees and show that they are not harder complexity-wise t...
متن کاملWeighted automata
Weighted automata are classical finite automata in which the transitions carry weights. 7 These weights may model quantitative properties like the amount of resources needed for executing 8 a transition or the probability or reliability of its successful execution. Using weighted automata, 9 we may also count the number of successful paths labeled by a given word. 10 As an introduction into thi...
متن کامل