A Polynomial Time Algorithm for Deciding the Equivalence Problem for 2-Tape Deterministic Finite State Acceptors

We provide a polynomial time algorithm for deciding the equation solvability problem over finite groups that are semidirect products of a [Formula: see text]-group and an Abelian group. As a consequence, we obtain a polynomial time algorithm for deciding the equivalence problem over semidirect products of a finite nilpotent group and a finite Abelian group. The key ingredient of the proof is to represent group expressions using a special polycyclic presentation of these finite solvable groups.

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INFIX-FREE REGULAR EXPRESSIONS AND LANGUAGES

International Journal of Foundations of Computer Science ◽

10.1142/s0129054106003887 ◽

2006 ◽

Vol 17 (02) ◽

pp. 379-393 ◽

Cited By ~ 16

Author(s):

YO-SUB HAN ◽

YAJUN WANG ◽

DERICK WOOD

Keyword(s):

Polynomial Time ◽

Regular Language ◽

Polynomial Time Algorithm ◽

Time Algorithm ◽

Regular Languages ◽

Finite State Automaton ◽

Primality Test ◽

Finite State ◽

State Pair ◽

Free Decomposition

We study infix-free regular languages. We observe the structural properties of finite-state automata for infix-free languages and develop a polynomial-time algorithm to determine infix-freeness of a regular language using state-pair graphs. We consider two cases: 1) A language is specified by a nondeterministic finite-state automaton and 2) a language is specified by a regular expression. Furthermore, we examine the prime infix-free decomposition of infix-free regular languages and design an algorithm for the infix-free primality test of an infix-free regular language. Moreover, we show that we can compute the prime infix-free decomposition in polynomial time. We also demonstrate that the prime infix-free decomposition is not unique.

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A polynomial-time algorithm for an equivalence problem which arises in hybrid systems theory

Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171) ◽

10.1109/cdc.1998.758526 ◽

2002 ◽

Cited By ~ 1

Author(s):

B. DasGupta ◽

E.D. Sontag

Keyword(s):

Systems Theory ◽

Hybrid Systems ◽

Polynomial Time ◽

Equivalence Problem ◽

Polynomial Time Algorithm ◽

Time Algorithm

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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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