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  • 1.
    Bengtson, Jesper
    et al.
    IT Univ Copenhagen, Copenhagen, Denmark..
    Parrow, Joachim
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computing Science.
    Weber, Tjark
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computing Science.
    Psi-Calculi in Isabelle2016In: Journal of automated reasoning, ISSN 0168-7433, E-ISSN 1573-0670, Vol. 56, no 1, p. 1-47Article in journal (Refereed)
    Abstract [en]

    This paper presents a mechanisation of psi-calculi, a parametric framework for modelling various dialects of process calculi including (but not limited to) the pi-calculus, the applied pi-calculus, and the spi calculus. psi-calculi are significantly more expressive, yet their semantics is as simple in structure as the semantics of the original pi-calculus. Proofs of meta-theoretic properties for psi-calculi are more involved, however, not least because psi-calculi (unlike simpler calculi) utilise binders that bind multiple names at once. The mechanisation is carried out in the Nominal Isabelle framework, an interactive proof assistant designed to facilitate formal reasoning about calculi with binders. Our main contributions are twofold. First, we have developed techniques that allow efficient reasoning about calculi that bind multiple names in Nominal Isabelle. Second, we have adopted these techniques to mechanise substantial results from the meta-theory of psi-calculi, including congruence properties of bisimilarity and the laws of structural congruence. To our knowledge, this is the most extensive formalisation of process calculi mechanised in a proof assistant to date.

  • 2. Brillout, Angelo
    et al.
    Kroening, Daniel
    Rümmer, Philipp
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computer Systems.
    Wahl, Thomas
    An interpolating sequent calculus for quantifier-free Presburger arithmetic2011In: Journal of automated reasoning, ISSN 0168-7433, E-ISSN 1573-0670, Vol. 47, no 4, p. 341-367Article in journal (Refereed)
    Abstract [en]

    Craig interpolation has become a versatile tool in formal verification, used for instance to generate program assertions that serve as candidates for loop invariants. In this paper, we consider Craig interpolation for quantifier-free Presburger arithmetic (QFPA). Until recently, quantifier elimination was the only available interpolation method for this theory, which is, however, known to be potentially costly and inflexible. We introduce an interpolation approach based on a sequent calculus for QFPA that determines interpolants by annotating the steps of an unsatisfiability proof with partial interpolants. We prove our calculus to be sound and complete. We have extended the Princess theorem prover to generate interpolating proofs, and applied it to a large number of publicly available Presburger arithmetic benchmarks. The results document the robustness and efficiency of our interpolation procedure. Finally, we compare the procedure against alternative interpolation methods, both for QFPA and linear rational arithmetic.

  • 3. Cok, David R.
    et al.
    Stump, Aaron
    Weber, Tjark
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computing Science.
    The 2013 Evaluation of SMT-COMP and SMT-LIB2015In: Journal of automated reasoning, ISSN 0168-7433, E-ISSN 1573-0670, Vol. 55, no 1, p. 61-90Article in journal (Refereed)
    Abstract [en]

    After 8 years of SMT Competitions, the SMT Steering Committee decided, for 2013, to sponsor an evaluation of the status of SMT benchmarks and solvers, rather than another competition. This report summarizes the results of the evaluation, conducted by the authors. The key observations are that (1) the competition results are quite sensitive to randomness and (2) the most significant need for the future is assessment and improvement of benchmarks in the light of SMT applications. The evaluation also measured competitiveness of solvers, general coverage of solvers, logics, and benchmarks, and degree of repeatability of measurements and competitions.

  • 4.
    Zeljic, Aleksandar
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computer Systems.
    Wintersteiger, Christoph M.
    Rümmer, Philipp
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computer Systems.
    An approximation framework for solvers and decision procedures2017In: Journal of automated reasoning, ISSN 0168-7433, E-ISSN 1573-0670, Vol. 58, no 1, p. 127-147Article in journal (Refereed)
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