Bit-Vector Optimization

Nadel, Alexander; Ryvchin, Vadim

doi:10.1007/978-3-662-49674-9_53

Cited by 25 publications

(45 citation statements)

References 25 publications

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“…We present our generalization of [31] to the case of signed/unsigned Bit-Vector Optimization, and then move on to deal with Floating-Point Optimization.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…Hereafter, we generalize the unsigned BV maximization procedures described in [31] to the case of signed and unsigned BV optimization. To this extent, we introduce the novel notion of BV attractor.…”

Section: Bit-vector Optimizationmentioning

confidence: 99%

“…Definitions 2 and 3 with Theorem 1 suggest thus a direct extension to the minimization/maximization of signed BV of the algorithm for unsigned BV in [31]: apply the unsigned-BV maximization [resp. minimization] algorithm of [31] to the objective obj def = (obj nxor n attr) [resp. obj def = (obj xor n attr)] instead than simply to obj [resp.…”

Section: Bit-vector Optimizationmentioning

confidence: 99%

“…In this paper, we consider two approaches for dealing with OMT(FP): a basic linear/binary search, based on the inline OMT schema for OMT(LRA ∪ T ) presented in [38], and Floating-Point Optimization with Binary Search (OFP-BS), a brand-new engine inspired by the OBV-BS algorithm for unsigned Bit-Vectors in [31] and by Theorem 2 and relative definitions in §3.2.…”

Section: Omt(f P) Proceduresmentioning

confidence: 99%

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Optimization Modulo the Theory of Floating-Point Numbers

Trentin

Sebastiani

2019

Lecture Notes in Computer Science

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Optimization Modulo Theories (OMT) is an important extension of SMT which allows for finding models that optimize given objective functions, typically consisting in linear-arithmetic or pseudo-Boolean terms. However, many SMT and OMT applications, in particular from SW and HW verification, require handling bit-precise representations of numbers, which in SMT are handled by means of the theory of Bit-Vectors (BV) for the integers and that of Floating-Point Numbers (FP) for the reals respectively. Whereas an approach for OMT with (unsigned) BV has been proposed by Nadel & Ryvchin, unfortunately we are not aware of any existing approach for OMT with FP. In this paper we fill this gap. We present a novel OMT approach, based on the novel concept of attractor and dynamic attractor, which extends the work of Nadel & Ryvchin to signed BV and, most importantly, to FP. We have implemented some OMT(BV) and OMT(FP) procedures on top of OPTIMATHSAT and tested the latter ones on modified problems from the SMT-LIB repository. The empirical results support the validity and feasibility of the novel approach. * We would like to thank the anonymous reviewers for their insightful comments and suggestions, and we thank Alberto Griggio for support with MATHSAT code. the bitwise representation of the objective, ordered from the most-significant bit (MSB) to the least-significant bit (LSB).In this paper we address -for the first time to the best of our knowledge-OMT for the theory of signed Bit-Vectors and, most importantly, for the theory of Floating-Point Arithmetic (OMT(FP)), by exploiting some properties of the two's complement encoding for signed BV and of the IEEE 754-2008 encoding for FP respectively.We start from introducing the notion of attractor, which represent (the bitwise encoding of) the target value for the objective which the optimization process aims at. This allows us for easily leverage the procedure of [31] to work with both signed and unsigned Bit-Vectors, by minimizing lexicographically the bitwise distance between the objective and the attractor, that is, by minimizing lexicographically the bitwise-xor between the objective and the attractor.Unfortunately there is no such notion of (fixed) attractor for FP numbers, because the target value moves as long as the bits of the objective are updated from the MSB to the LSB, and the optimization process may have to change dynamically its aim, even at the opposite direction. (For instance, as soon as the minimization process realizes there is no solution with a negative value for the objective and thus sets its MSB to 0, the target value is switched from −∞ to 0+, and the search switches direction, from the maximization of the exponent and the significand to their minimization.)To cope with this fact, we introduce the notions of dynamic attractor and attractor trajectory, representing the dynamics of the moving target value, which are progressively updated as soon as the bits of the objective are updated from the MSB to the LSB. Based on these ideas, we present novel OMT...

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“…We present our generalization of [31] to the case of signed/unsigned Bit-Vector Optimization, and then move on to deal with Floating-Point Optimization.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Section: Bit-vector Optimizationmentioning

confidence: 99%

Section: Bit-vector Optimizationmentioning

confidence: 99%

Section: Omt(f P) Proceduresmentioning

confidence: 99%

See 2 more Smart Citations

Optimization Modulo the Theory of Floating-Point Numbers

Trentin

Sebastiani

2019

Lecture Notes in Computer Science

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“…If the formula has no satisfiable assignments, LEXSAT proves it unsatisfiable. There are several solutions for the LEXSAT problem [13,24,25]. For our work, we use an efficient algorithm for generating consecutive LEXSAT assignments [25].…”

Section: Boolean Satisfiabilitymentioning

confidence: 99%

Progressive Generation of Canonical Irredundant Sums of Products Using a SAT Solver

Petkovska

Mishchenko

Novo

et al. 2017

Advanced Logic Synthesis

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We present an algorithm that progressively generates canonical irredundant Sums Of Products (SOPs) for completely-and incompletely-specified Boolean functions using a satisfiability (SAT) solver. The progressive generation allows for real time monitoring and early termination, as well as for generation of partial SOPs for incremental applications. On the other hand, canonicity brings independence of the original representation and often yields smaller and more regular SOPs that lead to smaller circuits after algebraic factoring. Also, canonicity is key in applications such as constraint solving and random assignment generation, which traditionally rely on methods based on Binary Decision Diagram (BDD). However, in contrast with BDDs, our algorithm can relax canonicity to improve speed and scalability. In general, our method is more scalable for benchmarks with many structurally isomorphic outputs. It also improves the quality of results up to 10%, in terms of the SOP size, compared to a state-of-the-art BDD-based method. Experiments with global circuit restructuring using SAT-based SOPs show that area-delay product can be improved up to 27%, compared to global restructuring using BDD-based SOPs.

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