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An interpolating theorem prover
 In TACAS
, 2004
"... Abstract. We present a method of deriving Craig interpolants from proofs in the quantifierfree theory of linear inequality and uninterpreted function symbols, and an interpolating theorem prover based on this method. The prover has been used for predicate refinement in the Blast software model chec ..."
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Cited by 101 (11 self)
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Abstract. We present a method of deriving Craig interpolants from proofs in the quantifierfree theory of linear inequality and uninterpreted function symbols, and an interpolating theorem prover based on this method. The prover has been used for predicate refinement in the Blast software model
Modularization and Interpolation
, 1998
"... Interpolation does not hold for first order arithmetic, but this does not affect modularization theorem due to Maibaum and Turski (dealing with pushouts of conservative extensions) for theories containing arithmetic, since this theorem does not in fact use Interpolation Theorem. We present a short p ..."
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in [1]. Theorem 1 Interpolation Theorem does not hold in first order arithmetic with additional predicate symbols. Proof . Let T (P ) be a formula of firstorder arithmetic with an additional unary predicate P stating that P satisfies standard inductive clauses of the truth definition for prenex
Discretely Ordered Modules as a FirstOrder Extension of the Cutting Planes Proof System
"... We define a firstorder extension LK(CP) of the cutting planes proof system CP as the firstorder sequent calculus LK whose atomic formulas are CPinequalities P i a i \Delta x i b (x i 's variables, a i 's and b constants). We prove an interpolation theorem for LK(CP) yielding as a ..."
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Cited by 12 (0 self)
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We define a firstorder extension LK(CP) of the cutting planes proof system CP as the firstorder sequent calculus LK whose atomic formulas are CPinequalities P i a i \Delta x i b (x i 's variables, a i 's and b constants). We prove an interpolation theorem for LK(CP) yielding as a
On Interpolation and Automatization for Frege Systems
, 2000
"... The interpolation method has been one of the main tools for proving lower bounds for propositional proof systems. Loosely speaking, if one can prove that a particular proof system has the feasible interpolation property, then a generic reduction can (usually) be applied to prove lower bounds for the ..."
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Cited by 49 (8 self)
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, neither Frege nor TC 0 Frege has the feasible interpolation property. In order to carry out our argument, we show how to carry out proofs of many elementary axioms/theorems of arithmetic in polynomial size TC 0 Frege. As a corollary, we obtain that TC 0 Frege as well as any proof system
Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic
"... A proof of the (propositional) Craig interpolation theorem for cutfree sequent calculus yields that a sequent with a cutfree proof (or with a proof with cutformulas of restricted form; in particular, with only analytic cuts) with k inferences has an interpolant whose circuitsize is at most k. We ..."
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Cited by 93 (4 self)
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. We give a new proof of the interpolation theorem based on a communication complexity approach which allows a similar estimate for a larger class of proofs. We derive from it several corollaries: 1. Feasible interpolation theorems for the following proof systems: (a) resolution. (b) a subsystem of LK
Borrowing Interpolation
, 2011
"... We present a generic method for establishing interpolation properties by ‘borrowing ’ across logical systems. The framework used is that of the socaled ‘institution theory’ which is a categorical abstract model theory providing a formal definition for the informal concept of ‘logical system’ and a ..."
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Cited by 4 (1 self)
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logic or in computing science, most of these interpolation properties apparently being new results. These logical systems include fragments of (classical many sorted) first order logic with equality, preordered algebra and its Horn fragment, partial algebra, higher order logic. Applications are also
Resolution Proof Transformation for Compression and Interpolation
"... Abstract. Verification methods based on SAT, SMT, and Theorem Proving often rely on proofs of unsatisfiability as a powerful tool to extract information in order to reduce the overall effort. For example a proof may be traversed to identify a minimal reason that led to unsatisfiability, for computi ..."
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, for computing abstractions, or for deriving Craig interpolants. In this paper we focus on two important aspects that concern efficient handling of proofs of unsatisfiability: compression and manipulation. First of all, since the proof size can be very large in general (exponential in the size of the input
Interpolated free group factors
 Pacific J. Math
, 1994
"... Abstract. The interpolated free group factors L(Fr) for 1 < r ≤ ∞, (also defined by F. Rădulescu) are given another (but equivalent) definition as well as proofs of their properties with respect to compression by projections and free products. In order to prove the addition formula for free produ ..."
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Cited by 60 (4 self)
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Abstract. The interpolated free group factors L(Fr) for 1 < r ≤ ∞, (also defined by F. Rădulescu) are given another (but equivalent) definition as well as proofs of their properties with respect to compression by projections and free products. In order to prove the addition formula for free
Algebraic Models of Computation and Interpolation for Algebraic Proof Systems
, 1998
"... this paper we are interested in systems that use uses polynomials instead of boolean formulas. From the previous list this includes the Nullstellensatz refutations. Recently a stronger system using polynomials was proposed, the polynomial calculus, also called the Groebner calculus [9]. The proof sy ..."
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Cited by 23 (3 self)
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systems using lower bounds on circuit complexity. This method is based on proving computationally efficient versions of Craig's interpolation theorem for the proof system in question [14, 18]. For appropriate tautologies the interpolation theorem
1Synthesizing Multiple Boolean Functions using Interpolation on a Single Proof
"... Abstract—It is often difficult to correctly implement a Boolean controller for a complex system, especially when concurrency is involved. Yet, it may be easy to formally specify a controller. For instance, for a pipelined processor it suffices to state that the visible behavior of the pipelined sys ..."
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system should be identical to a nonpipelined reference system (BurchDill paradigm). We present a novel procedure to efficiently synthesize multiple Boolean control signals from a specification given as a quantified firstorder formula (with a specific quantifier structure). Our approach uses
Results 1  10
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488