Adapting Real Quantifier Elimination Methods for Conflict Set Computation

The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance. One of the central problems is the computation of good explanations of the unsatisfiability of such sets, i.e.\ obtaining a small subset of the input constraints whose conjunction is already unsatisfiable. We adapt two commonly used real quantifier elimination methods, cylindrical algebraic decomposition and virtual substitution, to provide such conflict sets and demonstrate the performance of our method in practice

Enhancing Reuse of Constraint Solutions to Improve Symbolic Execution

Constraint solution reuse is an effective approach to save the time of constraint solving in symbolic execution. Most of the existing reuse approaches are based on syntactic or semantic equivalence of constraints; e.g. the Green framework is able to reuse constraints which have different representations but are semantically equivalent, through canonizing constraints into syntactically equivalent normal forms. However, syntactic/semantic equivalence is not a necessary condition for reuse--some constraints are not syntactically or semantically equivalent, but their solutions still have potential for reuse. Existing approaches are unable to recognize and reuse such constraints. In this paper, we present GreenTrie, an extension to the Green framework, which supports constraint reuse based on the logical implication relations among constraints. GreenTrie provides a component, called L-Trie, which stores constraints and solutions into tries, indexed by an implication partial order graph of constraints. L-Trie is able to carry out logical reduction and logical subset and superset querying for given constraints, to check for reuse of previously solved constraints. We report the results of an experimental assessment of GreenTrie against the original Green framework, which shows that our extension achieves better reuse of constraint solving result and saves significant symbolic execution time.Comment: this paper has been submitted to conference ISSTA 201

A study of systems implementation languages for the POCCNET system

The results are presented of a study of systems implementation languages for the Payload Operations Control Center Network (POCCNET). Criteria are developed for evaluating the languages, and fifteen existing languages are evaluated on the basis of these criteria

Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)

Oxford, UK, 26 August 200

A geometric constraint over k-dimensional objects and shapes subject to business rules

This report presents a global constraint that enforces rules written in a language based on arithmetic and first-order logic to hold among a set of objects. In a first step, the rules are rewritten to Quantifier-Free Presburger Arithmetic (QFPA) formulas. Secondly, such formulas are compiled to generators of k-dimensional forbidden sets. Such generators are a generalization of the indexicals of cc(FD). Finally, the forbidden sets generated by such indexicals are aggregated by a sweep-based algorithm and used for filtering. The business rules allow to express a great variety of packing and placement constraints, while admitting efficient and effective filtering of the domain variables of the k-dimensional object, without the need to use spatial data structures. The constraint was used to directly encode the packing knowledge of a major car manufacturer and tested on a set of real packing problems under these rules, as well as on a packing-unpacking problem