5,386 research outputs found
Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis
The safety of infinite state systems can be checked by a backward
reachability procedure. For certain classes of systems, it is possible to prove
the termination of the procedure and hence conclude the decidability of the
safety problem. Although backward reachability is property-directed, it can
unnecessarily explore (large) portions of the state space of a system which are
not required to verify the safety property under consideration. To avoid this,
invariants can be used to dramatically prune the search space. Indeed, the
problem is to guess such appropriate invariants. In this paper, we present a
fully declarative and symbolic approach to the mechanization of backward
reachability of infinite state systems manipulating arrays by Satisfiability
Modulo Theories solving. Theories are used to specify the topology and the data
manipulated by the system. We identify sufficient conditions on the theories to
ensure the termination of backward reachability and we show the completeness of
a method for invariant synthesis (obtained as the dual of backward
reachability), again, under suitable hypotheses on the theories. We also
present a pragmatic approach to interleave invariant synthesis and backward
reachability so that a fix-point for the set of backward reachable states is
more easily obtained. Finally, we discuss heuristics that allow us to derive an
implementation of the techniques in the model checker MCMT, showing remarkable
speed-ups on a significant set of safety problems extracted from a variety of
sources.Comment: Accepted for publication in Logical Methods in Computer Scienc
Mechanized semantics
The goal of this lecture is to show how modern theorem provers---in this
case, the Coq proof assistant---can be used to mechanize the specification of
programming languages and their semantics, and to reason over individual
programs and over generic program transformations, as typically found in
compilers. The topics covered include: operational semantics (small-step,
big-step, definitional interpreters); a simple form of denotational semantics;
axiomatic semantics and Hoare logic; generation of verification conditions,
with application to program proof; compilation to virtual machine code and its
proof of correctness; an example of an optimizing program transformation (dead
code elimination) and its proof of correctness
COSMICAH 2005: workshop on verification of COncurrent Systems with dynaMIC Allocated Heaps (a Satellite event of ICALP 2005) - Informal Proceedings
Lisboa Portugal, 10 July 200
Automata-theoretic and bounded model checking for linear temporal logic
In this work we study methods for model checking the temporal logic LTL. The focus is on the automata-theoretic approach to model checking and bounded model checking.
We begin by examining automata-theoretic methods to model check LTL safety properties. The model checking problem can be reduced to checking whether the language of a finite state automaton on finite words is empty. We describe an efficient algorithm for generating small finite state automata for so called non-pathological safety properties. The presented implementation is the first tool able to decide whether a formula is non-pathological. The experimental results show that treating safety properties can benefit model checking at very little cost. In addition, we find supporting evidence for the view that minimising the automaton representing the property does not always lead to a small product state space. A deterministic property automaton can result in a smaller product state space even though it might have a larger number states.
Next we investigate modular analysis. Modular analysis is a state space reduction method for modular Petri nets. The method can be used to construct a reduced state space called the synchronisation graph. We devise an on-the-fly automata-theoretic method for model checking the behaviour of a modular Petri net from the synchronisation graph. The solution is based on reducing the model checking problem to an instance of verification with testers. We analyse the tester verification problem and present an efficient on-the-fly algorithm, the first complete solution to tester verification problem, based on generalised nested depth-first search.
We have also studied propositional encodings for bounded model checking LTL. A new simple linear sized encoding is developed and experimentally evaluated. The implementation in the NuSMV2 model checker is competitive with previously presented encodings. We show how to generalise the LTL encoding to a more succint logic: LTL with past operators. The generalised encoding compares favourably with previous encodings for LTL with past operators. Links between bounded model checking and the automata-theoretic approach are also explored.reviewe
Distributed LTL Model Checking with Hash Compaction
AbstractWe extend a distributed-memory explicit-state LTL model checking algorithm (OWCTY) with hash compaction. We provide a detailed description of the improved algorithm and a correctness argument in the theoretical part of the paper. Additionally, we deliver an implementation of the algorithm as part of out parallel and distributed-memory model checker DiVinE, and use this implementation for a practical evaluation of the approach, on which we report in the experimental part of the paper
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