A polynomial time algorithm for the local testability problem of deterministic finite automata

1991 ◽  
Vol 40 (10) ◽  
pp. 1087-1093 ◽  
Author(s):  
S.M. Kim ◽  
R. McNaughton ◽  
R. McCloskey
Keyword(s):  
Polynomial Time ◽  
Finite Automata ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Deterministic Finite Automata

ORDINAL AUTOMATA AND CANTOR NORMAL FORM

2012 ◽  
Vol 23 (01) ◽  
pp. 87-98
Author(s):  
ZOLTÁN ÉSIK
Keyword(s):  
Normal Form ◽  
Polynomial Time ◽  
Regular Language ◽  
Finite Automata ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Order Type ◽  
Deterministic Finite Automaton ◽  
Lexicographic Ordering ◽  
Language L

It is known that an ordinal is the order type of the lexicographic ordering of a regular language if and only if it is less than ωω. We design a polynomial time algorithm that constructs, for each well-ordered regular language L with respect to the lexicographic ordering, given by a deterministic finite automaton, the Cantor Normal Form of its order type. It follows that there is a polynomial time algorithm to decide whether two deterministic finite automata accepting well-ordered regular languages accept isomorphic languages. We also give estimates on the state complexity of the smallest "ordinal automaton" representing an ordinal less than ωω, together with an algorithm that translates each such ordinal to an automaton.

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

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