-Calculus with Explicit Points and Approximations

Abstract

We present a Gentzen-style sequent calculus for program verification which accommodates both model checkinglike verification based on global state space exploration, and compositional reasoning. To handle the complexities arising from the presence of fixed-point formulas, programs with dynamically evolving architecture, and cut rules we use transition assertions, and introduce fixed-point approximants explicitly into the assertion language. We address, in a game-based manner, the semantical basis of this approach, as it applies to the entailment subproblem. Soundness and completeness results are obtained, and examples are shown illustrating some of the concepts.

Compositional Verification of Secure Applet Interactions

“…[16,8,9]). Let a range over applet name variables 4 , v over program point variables, π over applet call stack variables, Π over applet call stack terms generated by …”

“…Fixed-point formulae are handled as in [8] through fixed-point approximation by using explicit ordinal variables κ to represent approximation ordinals:…”

“…Informally, the discharge rule applies if (1) every non-axiom leaf of the proof tree is an instance (up to a substitution) of some ancestor sequent in the proof tree, (2) for each such sequent, this substitution maps some ordinal variable approximating a fixed-point formula to an ordinal variable which is assumed to be smaller, and (3) these separate induction schemes are consistent with each other. For the technical details the interested reader is referred to [8,7,9].…”

“…-a specification language based on the modal µ-calculus [12,8], together with a set of specification patterns, inspired from Bandera [1], that allows higherlevel specifications and reasoning; -a compositional proof system in the style of [16,7,9] that is used for proving correctness of property decompositions. This proof system has been proved sound w.r.t.…”

Reducing Behavioural to Structural Properties of Programs with Procedures

“…Our research is also related to previous work on tableau systems for the verification of infinite-state systems [6,20], model checking based on pushdown systems [5,7,8] or recursive state machines [2], temporal logics for nested calls and returns [3,1], interprocedural dataflow analysis [18], and abstract interpretation (cf. e.g., the completeness result of [17]).…”