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Verifying Communicating Multipushdown Systems
"... Abstract. Communicating multipushdown systems model networks of multithreaded recursive programs communicating via reliable FIFO channels. Hence their verification problems are undecidable in general. The behaviours of these systems can be represented as directed graphs, which subsume both Message ..."
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Abstract. Communicating multipushdown systems model networks of multithreaded recursive programs communicating via reliable FIFO channels. Hence their verification problems are undecidable in general. The behaviours of these systems can be represented as directed graphs, which subsume both Message Sequence Charts and nested words. We extend the notion of splitwidth [8] to these graphs, defining a simple algebra to compose/decompose these behaviours using two natural operations: shuffle and merge. We obtain simple, uniform and optimal decision procedures for various verification problems parametrized by splitwidth, ranging from reachability to modelchecking against MSO, PDL and Temporal Logics. 1
The PathWidth of Integer Linear Programming
"... Abstract. We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FOdefinable class of graphs. For each solution there may be many graphs representing it. However, one of these graphs is of pathwidth at ..."
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Abstract. We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FOdefinable class of graphs. For each solution there may be many graphs representing it. However, one of these graphs is of pathwidth at most 2n, where n is the number of variables in the instance. Since FO is decidable on graphs of bounded pathwidth, we obtain an alternative decidability result for ILP. The technique we use underlines a common principle to prove decidability which has previously been employed for automata with auxiliary storage. We also show how this new result links to automata theory and program verification. 1