
Optimization in SMT with LA(Q) Cost Functions
In the contexts of automated reasoning and formal verification, importan...
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Towards BitWidthIndependent Proofs in SMT Solvers
Many SMT solvers implement efficient SATbased procedures for solving fi...
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Nonlinear Real Arithmetic Benchmarks derived from Automated Reasoning in Economics
We consider problems originating in economics that may be solved automat...
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Manyopt: An Extensible Tool for Mixed, NonLinear Optimization Through SMT Solving
Optimization of MixedInteger NonLinear Programming (MINLP) supports im...
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A CDCLstyle calculus for solving nonlinear constraints
In this paper we propose a novel approach for checking satisfiability of...
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Monadic Decomposition in Integer Linear Arithmetic (Technical Report)
Monadic decomposability is a notion of variable independence, which asks...
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Structured Learning Modulo Theories
Modelling problems containing a mixture of Boolean and numerical variabl...
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Incomplete SMT Techniques for Solving NonLinear Formulas over the Integers
We present new methods for solving the Satisfiability Modulo Theories problem over the theory of QuantifierFree Nonlinear Integer Arithmetic, SMT(QFNIA), which consists in deciding the satisfiability of ground formulas with integer polynomial constraints. Following previous work, we propose to solve SMT(QFNIA) instances by reducing them to linear arithmetic: nonlinear monomials are linearized by abstracting them with fresh variables and by performing case splitting on integer variables with finite domain. For variables that do not have a finite domain, we can artificially introduce one by imposing a lower and an upper bound, and iteratively enlarge it until a solution is found (or the procedure times out). The key for the success of the approach is to determine, at each iteration, which domains have to be enlarged. Previously, unsatisfiable cores were used to identify the domains to be changed, but no clue was obtained as to how large the new domains should be. Here we explain two novel ways to guide this process by analyzing solutions to optimization problems: (i) to minimize the number of violated artificial domain bounds, solved via a MaxSMT solver, and (ii) to minimize the distance with respect to the artificial domains, solved via an Optimization Modulo Theories (OMT) solver. Using this SMTbased optimization technology allows smoothly extending the method to also solve MaxSMT problems over nonlinear integer arithmetic. Finally we leverage the resulting MaxSMT(QFNIA) techniques to solve ∃∀ formulas in a fragment of quantified nonlinear arithmetic that appears commonly in verification and synthesis applications.
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