Decidability of the unification problem for second-order languages with unary functional symbols

Zhezherun, A. P.

doi:10.1007/bf01071228

Cited by 3 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A.Zhezherun wrote a program to play with, and it worked surprisingly well! Besides, he studied the opportunity to formalize mathematical reasoning in a higher-order logic and proved in particular the decidability of the second-order monadic unification [39].…”

Section: Theoretical Workmentioning

confidence: 99%

Evidence Algorithm and System for Automated Deduction: A Retrospective View

Lyaletski

Verchinine

2010

Lecture Notes in Computer Science

View full text Add to dashboard Cite

A research project aimed at the development of an automated theorem proving system was started in Kiev (Ukraine) in early 1960s. The mastermind of the project, Academician V.Glushkov, baptized it "Evidence Algorithm", EA 3 . The work on the project lasted, off and on, more than 40 years. In the framework of the project, the Russian and English versions of the System for Automated Deduction, SAD, were constructed. They may be already seen as powerful theoremproving assistants. The paper 4 gives a retrospective view to the whole history of the development of the EA and SAD. Theoretical and practical results obtained on the long way are systematized. No comparison with similar projects is made.

show abstract

Section: Theoretical Workmentioning

confidence: 99%

Evidence Algorithm and System for Automated Deduction: A Retrospective View

Lyaletski

Verchinine

2010

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…Contrary to general SOU, MSOU is decidable [6,24,2]. In [23], it is proved that the problem is NP-hard.…”

mentioning

confidence: 99%

The Complexity of Monadic Second-Order Unification

Levy¹,

Schmidt-Schauß²,

Villaret³

2008

SIAM J. Comput.

View full text Add to dashboard Cite

Abstract. Monadic second-order unification is second-order unification where all function constants occurring in the equations are unary. Here we prove that the problem of deciding whether a set of monadic equations has a unifier is NP-complete, where we use the technique of compressing solutions using singleton context-free grammars. We prove that monadic second-order matching is also NP-complete.Key words. second-order unification, theorem proving, lambda calculus, context-free grammars, rewriting systems AMS subject classifications. 03B15, 68Q42, 68T15 DOI. 10.1137/0506454031. Introduction. The solvability of monadic second-order unification problems considered in this paper is a decision problem with many natural relationships with other well-known decision problems (higher-order unification, word unification, context unification and specializations thereof). For various members of this family, the exact complexity is still not known. In this paper we show that solvability of monadic second-order unification problems is NP-complete, thus adding a new piece to the larger puzzle. The techniques we use in our proof turned out to be relevant for other problems as well. Before we describe the organization of the paper we illuminate in more detail the relationship of monadic second-order unification with the above problems, give a brief survey on the techniques used in our proof, and indicate further contributions obtained from our method.

show abstract

“…The signature plays a crucial rule in this problem: Goldfarb's undecidability proof for Second-Order Unification [9,11] requires the use of a binary function symbol, whereas the first known decidable fragment of Second-Order Unification was Monadic Second-Order Unification, where function symbols can be at most unary [8,13,19,32]. In this work we reduce Second-Order Unification to Second-Order Unification with a signature that contains constants (0-ary function symbols) and just one binary function symbol.…”

Section: Introductionmentioning

confidence: 99%

Simplifying the signature in second-order unification

Levy

Villaret

2009

AAECC

View full text Add to dashboard Cite

Second-Order Unification is undecidable even for very specialized fragments. The signature plays a crucial role in these fragments. If all symbols are monadic, then the problem is NP-complete, whereas it is enough to have just one binary constant to lose decidability. In this work we reduce Second-Order Unification to Second-Order Unification with a signature that contains just one binary function symbol and constants. The reduction is based on partially currying the equations by using the binary function symbol for explicit application @. Our work simplifies the study of Second-Order Unification and some of its variants, like Context Unification and Bounded Second-Order Unification.

show abstract

Decidability of the unification problem for second-order languages with unary functional symbols

Cited by 3 publications

References 11 publications

Evidence Algorithm and System for Automated Deduction: A Retrospective View

Evidence Algorithm and System for Automated Deduction: A Retrospective View

The Complexity of Monadic Second-Order Unification

Simplifying the signature in second-order unification

Contact Info

Product

Resources

About