当前位置: X-MOL 学术Math. Struct. Comput. Sci. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Extensions of unification modulo ACUI
Mathematical Structures in Computer Science ( IF 0.5 ) Pub Date : 2019-11-11 , DOI: 10.1017/s0960129519000185
Franz Baader , Pavlos Marantidis , Antoine Mottet , Alexander Okhotin

The theory ACUI of an associative, commutative, and idempotent binary function symbol + with unit 0 was one of the first equational theories for which the complexity of testing solvability of unification problems was investigated in detail. In this paper, we investigate two extensions of ACUI. On one hand, we consider approximate ACUI-unification, where we use appropriate measures to express how close a substitution is to being a unifier. On the other hand, we extend ACUI-unification to ACUIG-unification, that is, unification in equational theories that are obtained from ACUI by adding a finite set G of ground identities. Finally, we combine the two extensions, that is, consider approximate ACUI-unification. For all cases we are able to determine the exact worst-case complexity of the unification problem.

中文翻译:

统一模 ACUI 的扩展

结合、交换、幂等二元函数符号+带单位的理论ACUI0是最早详细研究测试统一问题可解性的复杂性的方程理论之一。在本文中,我们研究了 ACUI 的两个扩展。一方面,我们考虑近似的 ACUI 统一,我们使用适当的度量来表达替代与统一的接近程度。另一方面,我们将 ACUI 统一扩展到 ACUIG 统一,即通过添加有限集从 ACUI 获得的等式理论的统一G地面身份。最后,我们结合这两个扩展,即考虑近似的 ACUI-unification。对于所有情况,我们都能够确定统一问题的确切最坏情况复杂性。
更新日期:2019-11-11
down
wechat
bug