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  1. Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning (SMT '08/BPR '08)
  2. Bit-precise reasoning with affine functions
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Implementing polymorphism in SMT solvers
BTOR: bit-precise modelling of word-level problems for model checking
Lemmas on demand for the extensional theory of arrays
A new testability guided abstraction to solving bit-vector formula
Deciding array formulas with frugal axiom instantiation
Bit-precise reasoning with affine functions
Using an SMT solver and Craig interpolation to detect and remove redundant linear constraints in representations of non-convex polyhedra
Towards an SMT proof format

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Bit-precise reasoning with affine functions

Content Provider ACM Digital Library
Author Kettle, Neil King, Andy
Abstract The class of affine Boolean functions is rich enough to express constant bits and dependencies between different bits of different words. For example, the function $(x_{0})$ ∧ $(¬y_{1})$ ∧ $(x_{4}$ ⇔ $y_{7})$ ∧ $(x_{5}$ ⇔ $¬y_{9})$ is affine and expresses the invariant that the low bit (bit 0) of the variable x is true, that bit 1 of y is false, that the bits 4 and 7 of x and y coincide whereas bits 5 and 9 of x and y differ. This class of Boolean function is amenable to bit-precise reasoning since it satisfies strong chain properties which bound the number of times a system of semantic fixpoint equations need to be reapplied when reasoning about loops. This paper address the key problem of abstracting an arbitrary Boolean function to either a general affine function or a so-called affine function of width 2, when the function is represented as an ROBDD. Novel algorithms are presented for this task: one that manipulates Boolean vectors and another which is inspired by anti-unification. The speed and precision of both algorithms are compared on benchmark circuits, to draw conclusions on the tractability of affine abstraction.
Starting Page 46
Ending Page 52
Page Count 7
File Format PDF
ISBN 9781605584409
DOI 10.1145/1512464.1512474
Language English
Publisher Association for Computing Machinery (ACM)
Publisher Date 2008-07-07
Publisher Place New York
Access Restriction Subscribed
Subject Keyword Propositional logic Model checking Abstract interpretation
Content Type Text
Resource Type Article
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