Skolem functions for factored formulas

John, Ajith K.; Shah, Sejal; Chakraborty, Supratik; Trivedi, Ashutosh; Akshay, S.

doi:10.1109/fmcad.2015.7542255

Cited by 26 publications

(56 citation statements)

References 7 publications

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“…. It has been argued in [14], [11], [2], [12] that the BFnS problem for F (X, Y) can be solved by first ordering the outputs, say as x 1 ≺ x 2 · · · ≺ x n , and then synthesizing a function…”

Section: ) Boolean Functional Synthesismentioning

confidence: 99%

“…Given a specification F (X, Y), sometimes it is easier to solve the BFnS problem for a "simpler" specification F(X, Y) such that a solution for F also serves as a solution for F . While "simplifications" of this nature have been used in earlier work [14], [1], [22], [7], we formalize this notion below as one of refinement.…”

Section: Refinement For Synthesismentioning

confidence: 99%

“…Suppose, Ψ n i+1 is not a correct Skolem function vector. In [14], it was shown that for any function vector ϕ n 1 , it is a Skolem function vector for F iff the error formula…”

Section: B Proof Of Theoremmentioning

confidence: 99%

“…While variants of the problem have been studied since long [17], [3], there has been significant recent interest in designing practically efficient algorithms for Boolean functional synthesis. The resulting breed of algorithms [14], [23], [22], [11], [25], [18], [13], [2], [1], [15], [7], [24] have been empirically shown to work well on large collections of benchmarks. Nevertheless, there are not-so-large examples that are currently not solvable within reasonable resources by any known algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Knowledge Compilation for Boolean Functional Synthesis

Akshay

Arora

Chakraborty

et al. 2019

2019 Formal Methods in Computer Aided Design (FMCAD)

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Given a Boolean formula F (X, Y), where X is a vector of outputs and Y is a vector of inputs, the Boolean functional synthesis problem requires us to compute a Skolem function vector Ψ(Y) for X such that F (Ψ(Y), Y) holds whenever ∃X F (X, Y) holds. In this paper, we investigate the relation between the representation of the specification F (X, Y) and the complexity of synthesis. We introduce a new normal form for Boolean formulas, called SynNNF, that guarantees polynomialtime synthesis and also polynomial-time existential quantification for some order of quantification of variables. We show that several normal forms studied in the knowledge compilation literature are subsumed by SynNNF, although SynNNF can be super-polynomially more succinct than them. Motivated by these results, we propose an algorithm to convert a specification in CNF to SynNNF, with the intent of solving the Boolean functional synthesis problem. Experiments with a prototype implementation show that this approach solves several benchmarks beyond the reach of state-of-the-art tools.• We present a new sub-class of negation normal form, called SynNNF, that admits polynomial-time synthesis and quantifier elimination for a set of variables.

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Section: ) Boolean Functional Synthesismentioning

confidence: 99%

Section: Refinement For Synthesismentioning

confidence: 99%

“…Suppose, Ψ n i+1 is not a correct Skolem function vector. In [14], it was shown that for any function vector ϕ n 1 , it is a Skolem function vector for F iff the error formula…”

Section: B Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Knowledge Compilation for Boolean Functional Synthesis

Akshay

Arora

Chakraborty

et al. 2019

2019 Formal Methods in Computer Aided Design (FMCAD)

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“…The ways to meet this challenge are usually to either merge factors that share variables [35] Work supported in part by NSF grants CCF-1319459 and IIS-1527668, by NSF Expeditions in Computing project "ExCAPE: Expeditions in Computer Augmented Program Engineering", by a grant from MHRD, Govt of India, under the IMPRINT-1 scheme, and by the Brazilian agency CNPq through the Ciência Sem Fronteiras program. or perform additional computations in order to combine the functions synthesized for different factors [19]. All these result in additional work that must be performed during the synthesis.…”

Section: Introductionmentioning

confidence: 99%

Functional Synthesis via Input-Output Separation

Chakraborty

Fried

Tabajara

et al. 2018

2018 Formal Methods in Computer Aided Design (FMCAD)

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Boolean functional synthesis is the process of constructing a Boolean function from a Boolean specification that relates input and output variables. Despite significant recent developments in synthesis algorithms, Boolean functional synthesis remains a challenging problem even when state-of-the-art methods are used for decomposing the specification. In this work we bring a fresh decomposition approach, orthogonal to existing methods, that explores the decomposition of the specification into separate input and output components. We make use of an input-output decomposition of a given specification described as a CNF formula, by alternatingly analyzing the separate input and output components. We exploit well-defined properties of these components to ultimately synthesize a solution for the entire specification. We first provide a theoretical result that, for input components with specific structures, synthesis for CNF formulas via this framework can be performed more efficiently than in the general case. We then show by experimental evaluations that our algorithm performs well also in practice on instances which are challenging for existing state-of-the-art tools, serving as a good complement to modern synthesis techniques.

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Manthan: A Data-Driven Approach for Boolean Function Synthesis

Golia

Roy

Meel

2020

Computer Aided Verification

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Boolean functional synthesis is a fundamental problem in computer science with wide-ranging applications and has witnessed a surge of interest resulting in progressively improved techniques over the past decade. Despite intense algorithmic development, a large number of problems remain beyond the reach of the state of the art techniques. Motivated by the progress in machine learning, we propose Manthan, a novel data-driven approach to Boolean functional synthesis. Manthan views functional synthesis as a classification problem, relying on advances in constrained sampling for data generation, and advances in automated reasoning for a novel proof-guided refinement and provable verification. On an extensive and rigorous evaluation over 609 benchmarks, we demonstrate that Manthan significantly improves upon the current state of the art, solving 356 benchmarks in comparison to 280, which is the most solved by a state of the art technique; thereby, we demonstrate an increase of 76 benchmarks over the current state of the art. Furthermore, Manthan solves 60 benchmarks that none of the current state of the art techniques could solve. The significant performance improvements, along with our detailed analysis, highlights several interesting avenues of future work at the intersection of machine learning, constrained sampling, and automated reasoning.

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Skolem functions for factored formulas

Cited by 26 publications

References 7 publications

Knowledge Compilation for Boolean Functional Synthesis

Knowledge Compilation for Boolean Functional Synthesis

Functional Synthesis via Input-Output Separation

Manthan: A Data-Driven Approach for Boolean Function Synthesis

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