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Completion of Rewrite Systems with Membership Constraints Part II: Constraint Solving
 J. Symbolic Computation
, 1992
"... this paper is to show how to solve the constraints that are involved in the deduction mechanism of the first part. This may be interesting in its own since this provides with a unification algorithm for an ordersorted logic with context variables and can be read independently of the first part. Thi ..."
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Cited by 71 (2 self)
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this paper is to show how to solve the constraints that are involved in the deduction mechanism of the first part. This may be interesting in its own since this provides with a unification algorithm for an ordersorted logic with context variables and can be read independently of the first part. This can also be compared with unification of term schemes of various kind (Chen & Hsiang, 1991; Salzer, 1992; Comon, 1995; R. Galbav'y and M. Hermann, 1992). Indeed,
The Undecidability of kProvability
 Annals of Pure and Applied Logic
, 1989
"... The kprovability problem is, given a first order formula φ and an integer k, to determine if φ has a proof consisting of k or fewer lines (i.e., formulas or sequents). This paper shows that the kprovability problem for the sequent calculus is undecidable. Indeed, for every r.e. srt ..."
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Cited by 35 (0 self)
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The kprovability problem is, given a first order formula &phi; and an integer k, to determine if &phi; has a proof consisting of k or fewer lines (i.e., formulas or sequents). This paper shows that the kprovability problem for the sequent calculus is undecidable. Indeed, for every r.e. srt X...
Decidability of Bounded Second Order Unification
 FB INFORMATIK, J.W. GOETHEUNIVERSITAT FRANKFURT AM MAIN
, 1999
"... It is wellknown that first order unification is decidable, whereas second order (and higherorder) unification is undecidable. Bounded second order unification (BSOU) is second order unification under the restriction that only a bounded number of holes in the instantiating terms for second order va ..."
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Cited by 9 (2 self)
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It is wellknown that first order unification is decidable, whereas second order (and higherorder) unification is undecidable. Bounded second order unification (BSOU) is second order unification under the restriction that only a bounded number of holes in the instantiating terms for second order variables is permitted, however, the size of the instantiation is not restricted. In this paper, a decision algorithm for bounded second order unification is described. This is the first nontrivial decidability result for second order unification, where the (finite) signature is not restricted and there are no restrictions on the occurrences of variables. We show that the monadic second order unification (MSOU), a specialization of BSOU is in \Sigma p 2. Since MSOU is related to word unification, this is compares favourably to the best known upper bound NEXPTIME (and also to the announced upper bound PSPACE) for word unification. This supports the claim that bounded second order unification is easier than context unification, whose decidability is currently an open question.
Decidability of Bounded HigherOrder Unification
, 2002
"... It is shown that unifiability of terms in the simply typed lambda calculus with beta and eta rules becomes decidable if there is a bound on the number of bound variables and lambdas in a unifier in etaexpanded betanormal form. ..."
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Cited by 8 (0 self)
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It is shown that unifiability of terms in the simply typed lambda calculus with beta and eta rules becomes decidable if there is a bound on the number of bound variables and lambdas in a unifier in etaexpanded betanormal form.
Bounded Arithmetic, Proof Complexity and Two Papers of Parikh
, 2002
"... This article surveys R. Parikh's work on feasibility, bounded arithmetic and the complexity of proofs. We discuss in depth two of Parikh's papers on these subjects and some of the subsequent progress in the areas of feasible arithmetic and lengths of proofs. ..."
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This article surveys R. Parikh's work on feasibility, bounded arithmetic and the complexity of proofs. We discuss in depth two of Parikh's papers on these subjects and some of the subsequent progress in the areas of feasible arithmetic and lengths of proofs.