Unification in commutative idempotent monoids

Baader, Franz; Büttner, Wolfram

doi:10.1016/0304-3975(88)90140-5

Cited by 24 publications

(28 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper we extend uni cation, the core mechanism of logic programming, to handle bags and sets. When bags and sets are represented with using the union operations, bag and set uni cation is a particular case of AC1and ACI1-uni cation, which has been extensively studied 44,25,24,10,33,18]. Recently, a n umber of uni cation algorithms have been introduced for various domains of bags and sets built with the bag and set constructors similar to the list constructor used in functional and logic programming 21,22,45,9].…”

Section: Introductionmentioning

confidence: 99%

A Nondeterministic Polynomial-Time Unification Algorithm for Bags, Sets and Trees

Dantsin

Воронков

1999

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Uni cation in logic programming deals with tree-like data represented by terms. Some applications, including deductive databases, require handling more complex values, for example nite sets or bags (nite multisets). We extend uni cation to the combined domain of bags, sets and trees in which bags and sets are generated by constructors similar to the list constructor. Our uni cation algorithm is presented as a nondeterministic polynomial-time algorithm that solves equality constraints in the spirit of the Martelli and Montanari algorithm.

show abstract

Section: Introductionmentioning

confidence: 99%

A Nondeterministic Polynomial-Time Unification Algorithm for Bags, Sets and Trees

Dantsin

Воронков

1999

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…The implication from left to right in (I); The pair ( * v * , * w) is the only pair from {h(v, w)} ∪ G such that both 1 The reduction given in [7] is slightly different. The first pair (v 0 , w 0 ) from G has two corresponding pairs (v * 0 , * w 0 ) and ( * v * 0 , * w 0 ) in G .…”

Section: Theorem 31 There Exists a Set Of Pairs Of Wordsmentioning

confidence: 97%

“…Unification modulo ACI is a well-studied problem. The paper [1] gives an algorithm for solving ACI-unification with constants and a doubly exponential upper bound on the number of most general ACI-unifiers. The doubly exponential upper bound is tight.…”

Section: Letmentioning

confidence: 99%

E-unification with Constants vs. General E-unification

Otop

2010

J Autom Reasoning

View full text Add to dashboard Cite

We present a solution to Problem #66 from the RTA open problem list. The question is whether there exists an equational theory E such that Eunification with constants is decidable but general E-unification is undecidable. The answer is positive and we show such a theory. The problem has several equivalent formulations, therefore the solution has many consequences. Our result also shows, that there exist two theories E 1 and E 2 over disjoint signatures, such that E 1 -unification with constants and E 2 -unification with constants are decidable, but (E 1 ∪ E 2 )-unification with constants is undecidable.

show abstract

“…This work mostly deals with AC unification-by reducing it to the solution of Diophantine equations-and only in the end it suggests a solution of the ACI problem, by replacing arithmetic equations with Boolean equations. Direct solutions of the ACI problem have been proposed by Büttner (Büttner 1986) and Baader and Büttner (Baader and Büttner 1988).…”

Section: Unification Algorithmsmentioning

confidence: 99%

“…2. If the test succeeds, then a solution can be constructed by assigning to each variable X in s = t a term composed of the union of all the constants present in s = t . For further details the reader is referred to (Baader and Büttner 1988).…”

Section: Examplementioning

confidence: 99%

Set unification

Dovier¹,

Pontelli²,

Rossi³

2006

Theory and Practice of Logic Programming

View full text Add to dashboard Cite

The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas-e.g., deductive databases, theorem proving, static analysis, rapid software prototyping. The various solutions proposed are spread across a large literature. In this paper we provide a uniform presentation of unification of sets, formalizing it at the level of set theory. We address the problem of deciding existence of solutions at an abstract level. This provides also the ability to classify different types of set unification problems. Unification algorithms are uniformly proposed to solve the unification problem in each of such classes.The algorithms presented are partly drawn from the literature-and properly revisited and analyzed-and partly novel proposals. In particular, we present a new goal-driven algorithm for general ACI 1 unification and a new simpler algorithm for general (Ab)(C ℓ) unification.

show abstract

Unification in commutative idempotent monoids

Cited by 24 publications

References 6 publications

A Nondeterministic Polynomial-Time Unification Algorithm for Bags, Sets and Trees

A Nondeterministic Polynomial-Time Unification Algorithm for Bags, Sets and Trees

E-unification with Constants vs. General E-unification

Set unification

Contact Info

Product

Resources

About