Hardness results for the subpower membership problem
نویسندگان
چکیده
منابع مشابه
The Subpower Membership Problem for Mal'cEV Algebras
Given tuples a1, . . . , ak and b in A n for some algebraic structure A, the subpower membership problem asks whether b is in the subalgebra of An that is generated by a1, . . . , ak . For A a finite group, there is a folklore algorithm which decides this problem in time polynomial in n and k. We show that the subpower membership problem for any finite Mal’cev algebra is in NP and give a polyno...
متن کاملThe subpower membership problem for semigroups
Fix a finite semigroup S and let a1, . . . , ak , b be tuples in a direct power S. The subpower membership problem (SMP) asks whether b can be generated by a1, . . . , ak. If S is a finite group, then there is a folklore algorithm that decides this problem in time polynomial in nk. For semigroups this problem always lies in PSPACE. We show that the SMP for a full transformation semigroup on 3 o...
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The subalgebra membership problem is the problem of deciding if a given element belongs to an algebra given by a set of generators. This is one of the best established computational problems in algebra. We consider a variant of this problem, which is motivated by recent progress in the Constraint Satisfaction Problem, and is often referred to as the Subpower Membership Problem (SMP). In the SMP...
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Fix a finite semigroup S and let a1, . . . , ak , b be tuples in a direct power S. The subpower membership problem (SMP) for S asks whether b can be generated by a1, . . . , ak. For combinatorial Rees matrix semigroups we establish a dichotomy result: if the corresponding matrix is of a certain form, then the SMP is in P; otherwise it is NP-complete. For combinatorial Rees matrix semigroups wit...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2018
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196718500339