# Verification of Flat FIFO Systems

The decidability and complexity of reachability problems and model-checking for flat counter systems have been explored in detail. However, only few results are known for flat FIFO systems, only in some particular cases (a single loop or a single bounded expression). We prove, by establishing reductions between properties, and by reducing SAT to a subset of these properties that many verification problems like reachability, non-termination, unboundedness are Np-complete for flat FIFO systems, generalizing similar existing results for flat counter systems. We construct a trace-flattable counter system that is bisimilar to a given flat FIFO system, which allows to model-check the original flat FIFO system. Our results lay the theoretical foundations and open the way to build a verification tool for (general) FIFO systems based on analysis of flat subsystems. 2012 ACM Subject Classification Theory of computation → Parallel computing models 1 Introduction FIFO systems Asynchronous distributed processes communicating through First In First Out (FIFO) channels are used since the seventies as models for protocols [40], distributed and concurrent programming and more recently for web service choreography interface [14]. Since FIFO systems simulate counter machines, most reachability properties are undecidable for FIFO systems: for example, the basic task of checking if the number of messages buffered in a channel can grow unboundedly is undecidable [13]. There aren't many interesting and useful FIFO subclasses with a decidable reachability problem. Considering FIFO systems with a unique FIFO channel is not a useful restriction since they may simulate Turing machines [13]. A few examples of decidable subclasses are half-duplex systems [15] (but they are restricted to two machines since the natural extension to three machines leads to undecidability), existentially bounded deadlock free FIFO systems [31] (but it is undecidable to check if a system is existentially bounded, even for deadlock free FIFO systems), synchronisable FIFO systems (the property of synchronisability is undecidable [28] and moreover, it is not clear which properties of synchronisable systems are decidable), flat FIFO systems [8, 9] and lossy FIFO systems [2] (but one loses the perfect FIFO mechanism).

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