Ground Interpolation for the Theory of Equality

Fuchs, Alexander; Goel, Amit; Grundy, Jim; Krstić, Sava; Tinelli, Cesare

doi:10.1007/978-3-642-00768-2_34

Cited by 29 publications

(29 citation statements)

References 22 publications

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“…When computing the partial interpolants of the theory lemmas, we internally split the mixed literals according to Section 3.2. Then we use an algorithm similar to [11] to compute an interpolant. This algorithm basically summarises the Aequalities that are adjacent on the path of equalities.…”

Section: Leaf Interpolationmentioning

confidence: 99%

Proof Tree Preserving Tree Interpolation

Christ

Hoenicke

2016

J Autom Reasoning

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Craig interpolation in SMT is difficult because, e. g., theory combination and integer cuts introduce mixed literals, i. e., literals containing local symbols from both input formulae. In this paper, we present a scheme to compute Craig interpolants in the presence of mixed literals. Contrary to existing approaches, this scheme neither limits the inferences done by the SMT solver, nor does it transform the proof tree before extracting interpolants. Our scheme works for the combination of uninterpreted functions and linear arithmetic but is extendable to other theories. The scheme is implemented in the interpolating SMT solver SMTInterpol.

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Section: Leaf Interpolationmentioning

confidence: 99%

Proof Tree Preserving Tree Interpolation

Christ

Hoenicke

2016

J Autom Reasoning

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“…Given a set A of atoms, we can use the well-known congruence-closure algorithm to construct a congruence graph [8] according to the following definition.…”

Section: Transitivity-congruence Chainsmentioning

confidence: 99%

Synthesizing multiple boolean functions using interpolation on a single proof

Hofferek

Gupta

Könighofer

et al. 2013

2013 Formal Methods in Computer-Aided Design

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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 system should be identical to a nonpipelined reference system (Burch-Dill paradigm). We present a novel procedure to efficiently synthesize multiple Boolean control signals from a specification given as a quantified first-order formula (with a specific quantifier structure). Our approach uses uninterpreted functions to abstract details of the design. We construct an unsatisfiable SMT formula from the given specification. Then, from just one proof of unsatisfiability, we use a variant of Craig interpolation to compute multiple coordinated interpolants that implement the Boolean control signals. Our method avoids iterative learning and back-substitution of the control functions. We applied our approach to synthesize a controller for a simple two-stage pipelined processor, and present first experimental results.

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“…Ground interpolation procedures for specific theories have been developed, e.g., for linear arithmetic over reals [23,38] and integers [8,9], uninterpreted functions with equality [19,38,50], functional lists [50], as well as, combinations of these theories [11,21,38,50]. These are the procedures that our approach builds on.…”

Section: Related Workmentioning

confidence: 99%

“…Modern SMT solvers implement ground interpolation procedures for the theories that are most commonly used in program verification. This includes theories such as linear arithmetic [8,9,23,38], the theory of uninterpreted function symbols with equality [19,38,50], and combinations of such theories [11,21,38,50]. However, many application-specific theories remain unsupported.…”

Section: Introductionmentioning

confidence: 99%

Complete instantiation-based interpolation

TotlaNishant

WiesThomas

2013

SIGPLAN Not.

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Craig interpolation has been a valuable tool for formal methods with interesting applications in program analysis and verification. Modern SMT solvers implement interpolation procedures for the theories that are most commonly used in these applications. However, many application-specific theories remain unsupported, which limits the class of problems to which interpolation-based techniques apply. In this paper, we present a generic framework to build new interpolation procedures via reduction to existing interpolation procedures. We consider the case where an application-specific theory can be formalized as an extension of a base theory with additional symbols and axioms. Our technique uses finite instantiation of the extension axioms to reduce an interpolation problem in the theory extension to one in the base theory. We identify a modeltheoretic criterion that allows us to detect the cases where our technique is complete. We discuss specific theories that are relevant in program verification and that satisfy this criterion. In particular, we obtain complete interpolation procedures for theories of arrays and linked lists. The latter is the first complete interpolation procedure for a theory that supports reasoning about complex shape properties of heap-allocated data structures. We have implemented this procedure in a prototype on top of existing SMT solvers and used it to automatically infer loop invariants of list-manipulating programs.

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Ground Interpolation for the Theory of Equality

Cited by 29 publications

References 22 publications

Proof Tree Preserving Tree Interpolation

Proof Tree Preserving Tree Interpolation

Synthesizing multiple boolean functions using interpolation on a single proof

Complete instantiation-based interpolation

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