197 research outputs found
A Uniform Substitution Calculus for Differential Dynamic Logic
This paper introduces a new proof calculus for differential dynamic logic
(dL) that is entirely based on uniform substitution, a proof rule that
substitutes a formula for a predicate symbol everywhere. Uniform substitutions
make it possible to rely on axioms rather than axiom schemata, substantially
simplifying implementations. Instead of nontrivial schema variables and
soundness-critical side conditions on the occurrence patterns of variables, the
resulting calculus adopts only a finite number of ordinary dL formulas as
axioms. The static semantics of differential dynamic logic is captured
exclusively in uniform substitutions and bound variable renamings as opposed to
being spread in delicate ways across the prover implementation. In addition to
sound uniform substitutions, this paper introduces differential forms for
differential dynamic logic that make it possible to internalize differential
invariants, differential substitutions, and derivations as first-class axioms
in dL
A Vision of Collaborative Verification-Driven Engineering of Hybrid Systems
Abstract. Hybrid systems with both discrete and continuous dynamics are an important model for real-world physical systems. The key challenge is how to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires significant human guidance, since hybrid systems verification tools solve undecidable problems. It is thus not uncommon for verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) modeling hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks.
Quantifier Elimination over Finite Fields Using Gr\"obner Bases
We give an algebraic quantifier elimination algorithm for the first-order
theory over any given finite field using Gr\"obner basis methods. The algorithm
relies on the strong Nullstellensatz and properties of elimination ideals over
finite fields. We analyze the theoretical complexity of the algorithm and show
its application in the formal analysis of a biological controller model.Comment: A shorter version is to appear in International Conference on
Algebraic Informatics 201
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