Matching Modulo Associativity and Idempotency Is NP-Complete
نویسندگان
چکیده
We show that AI–matching (AI denotes the theory of an associative and idempotent function symbol), which is solving matching word equations in free idempotent semigroups, is NP-complete. Note: this is a full version of the paper [9] and a revision of [8].
منابع مشابه
Unification and Matching Modulo Nilpotence
We consider equational uniication and matching problems where the equational theory contains a nilpotent function, i.e., a function f satisfying f(x;x) = 0 where 0 is a constant. Nilpotent matching and uniication are shown to be NP-complete. In the presence of associativity and commutativity, the problems still remain NP-complete. But when 0 is also assumed to be the unity for the function f, t...
متن کاملUnication Problems Modulo a Theory of Until
We refer to this equational theory as W . We came across these axioms while studying identities or equivalences in Linear Temporal Logic (LTL) — a logic for reasoning about time with the “until” operator U , but without the “next-time” operator ©. It is not hard to see that the until operator U satisfies these identities. However, note that there are other models for these identities as well: t...
متن کاملOn the computational complexity of finding a minimal basis for the guess and determine attack
Guess-and-determine attack is one of the general attacks on stream ciphers. It is a common cryptanalysis tool for evaluating security of stream ciphers. The effectiveness of this attack is based on the number of unknown bits which will be guessed by the attacker to break the cryptosystem. In this work, we present a relation between the minimum numbers of the guessed bits and uniquely restricted...
متن کاملTheorem Proving modulo Associativity
We present an inference system for rst-order constrained clauses with equality modulo associativity (A). Our procedure is refutationally complete and reduces to Knuth-Bendix completion modulo A in the equational case. As an essential ingredient we present the rst |as far as we know| A-compatible reduction ordering total on the ground A-congruence classes.
متن کاملAnti-pattern Matching Modulo
Negation is intrinsic to human thinking and most of the time when searching for something, we base our patterns on both positive and negative conditions. In a recent work, the notion of term was extended to the one of anti-term, i.e. terms that may contain complement symbols. Here we generalize the syntactic anti-pattern matching to anti-pattern matching modulo an arbitrary equational theory E ...
متن کامل