Verifying Programs with Unreliable Channels

Abstract

We consider the veri cation of a particular class of in nite-state systems, namely systems consisting of nite-state processes that communicate via unbounded lossy FIFO channels. This class is able to model e.g. link protocols such as the Alternating Bit Protocol and HDLC. For this class of systems, we show that several interesting veri cation problems are decidable by giving algorithms for verifying (1) the reachability problem: is a nite set of global states reachable from some other global state of the system, (2) safety properties over traces formulated as regular sets of allowed nite traces, and (3) eventuality properties: do all computations of a system eventually reach a given set of states. We have used the algorithms to verify some idealized sliding-window protocols with reasonable time and space resources. Our results should be contrasted with the well-known fact that these problems are undecidable for systems with unbounded perfect FIFO channels.

Computable fixpoints in well-structured symbolic model checking

“…Lossy channel systems (LCS's) are another classic model for which WSTS theory provides many positive results [9,31]. In this section, we first recall the necessary notations, definitions and classical results before considering the verification of game-theoretical and probabilistic properties in Sects.…”

“…(37), we opt for a semantics where message losses occur anywhere in the channels, right after a perfect step. In the literature, one often considers more liberal definitions with arbitrary losses before and after a step [9], or more restrictive definitions where messages can only be lost during the steps that (try to) send them to a channel [33] or when they are in position to be read at the head of a channel [45]. There is usually no essential semantical difference between these definitions that package the same atomic events into different single "steps".…”

Extrapolating (omega-)regular model checking

“…The idea for the encoding is as follows. Any integer number can be encoded in binary, 4 and the resulting sequence of 0 and 1 can be interpreted as a finite word. The procedure assumes that any number is represented by an infinite sequence of words.…”

“…Among the techniques to compute accelerations, one distinguishes between domain specific and generic techniques. Domain-specific techniques [22] exploit the specific properties and representations of the domain being considered and were for instance obtained for systems with queues in [23,33], for systems with integers and reals in [19,25,31], for pushdown systems in [32,53], and for lossy queues in [4]. Generic techniques consider automata-based representations and provide algorithms that operate directly on these representations, mostly disregarding the domain for which it is used.…”

Generalized Post Embedding Problems

“…We recall that PEP was introduced for UCSs, unidirectional channel systems where tests on channels are not supported [9,10], and that PEP dir corresponds to LCSs, i.e., lossy channel systems, for which decidability use techniques from WSTS theory [3,6,11,14]. Figure 1 depicts the resulting situation.…”