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From Local Search to Quantifier Elimination for Bit-Vectors in SMT Niemetz, Aina
Description
Many applications in hardware and software verification rely on Satisfiability Modulo Theories (SMT) solvers for bit-precise reasoning. For solving quantifier-free bit-vector formulas, current state-of-the-art is a technique called bit-blasting, which eagerly translates a given formula into propositional logic (SAT). Bit-blasting is efficient in practice, but may not scale if the input size can not be reduced sufficiently during preprocessing. For quantified bit-vector logics, the majority of solvers employ instantiation-based techniques, which aim to find conflicting ground instances of quantified formulas. For that, it is crucial to select good instantiations for the universal variables, or else the solver may be overwhelmed by the number of ground instances generated. In this talk I will present a complete propagation-based local search approach for quantifier-free bit-vector formulas. It utilizes conditional inverse value computation on concrete assignments for down-propagation. Computing inverse values of bit-vector operators is not always possible, but we can derive conditions that precisely characterize when bit-vector constraints are invertible. We utilized syntax-guided synthesis techniques to aid in establishing these conditions and verified them independently by using several SMT solvers. I will show how such invertibility conditions can be embedded into quantifier instantiations using Hilbert choice expressions.
Item Metadata
Title |
From Local Search to Quantifier Elimination for Bit-Vectors in SMT
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-08-31T10:17
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Description |
Many applications in hardware and software verification rely on
Satisfiability Modulo Theories (SMT) solvers for bit-precise reasoning.
For solving quantifier-free bit-vector formulas, current
state-of-the-art is a technique called bit-blasting, which eagerly
translates a given formula into propositional logic (SAT). Bit-blasting
is efficient in practice, but may not scale if the input size can not be
reduced sufficiently during preprocessing. For quantified bit-vector
logics, the majority of solvers employ instantiation-based techniques,
which aim to find conflicting ground instances of quantified formulas.
For that, it is crucial to select good instantiations for the universal
variables, or else the solver may be overwhelmed by the number of ground
instances generated.
In this talk I will present a complete propagation-based local search
approach for quantifier-free bit-vector formulas. It utilizes
conditional inverse value computation on concrete assignments for
down-propagation.
Computing inverse values of bit-vector operators is not always possible,
but we can derive conditions that precisely characterize when bit-vector
constraints are invertible. We utilized syntax-guided synthesis
techniques to aid in establishing these conditions and verified them
independently by using several SMT solvers. I will show how such
invertibility conditions can be embedded into quantifier instantiations
using Hilbert choice expressions.
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Extent |
24.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Stanford University
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Series | |
Date Available |
2019-04-06
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0377867
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International