On termination and invariance for faulty channel machines

Abstract

A channel machine consists of a finite controller together with several fifo channels; the controller can read messages from the head of a channel and write messages to the tail of a channel. In this paper we focus on channel machines with insertion errors, i.e., machines in whose channels messages can spontaneously appear. We consider the invariance problem: does a given insertion channel machine have an infinite computation all of whose configurations satisfy a given predicate? We show that this problem is primitive-recursive if the predicate is closed under message losses. We also give a non-elementary lower bound for the invariance problem under this restriction. Finally, using the previous result, we show that the satisfiability problem for the safety fragment of Metric Temporal Logic is non-elementary.

Safety alternating automata on data words

“…Satisfiability (over timed ω-words) for the safety fragment of metric temporal logic (MTL) was shown decidable in [Ouaknine and Worrell 2006], and nonelementary in [Bouyer et al 2008] by reducing from termination of channel machines with emptiness testing and insertion errors. It would be interesting to investigate whether · R. Lazić ideas in the proof of Theorem 3.3 above can be combined with those in the proof of primitive recursiveness of termination of channel machines with occurrence testing and insertion errors [Bouyer et al 2008] to obtain that satisfiability for safety MTL is primitive recursive.…”

“…It would be interesting to investigate whether · R. Lazić ideas in the proof of Theorem 3.3 above can be combined with those in the proof of primitive recursiveness of termination of channel machines with occurrence testing and insertion errors [Bouyer et al 2008] to obtain that satisfiability for safety MTL is primitive recursive.…”

Zeno, Hercules, and the Hydra

“…In [Bouyer et al 2012] it is shown that termination for insertion channel machines with emptiness tests is primitive recursive, though non-elementary. 3 This result is used to give a non-elementary lower bound in F 3 for the satisfiability problem for safety MTL.…”

“…Unlike [Bouyer et al 2012], we consider channel machines with a single channel. In [Bouyer et al 2012], without the hypothesis of fairness, the termination problem was shown to be non-elementary in the number of channels.…”

Reasoning with Time Intervals: A Logical and Computational Perspective

“…Adapting it to AE (and therefore, by symmetry, to AB) is then straightforward. As a note, let us recall that incrementing counter automata can be considered a variant of lossy counter automata in which faulty transitions increase the values instead of decrementing them; a comprehensive survey on faulty machines and on the complexity, decidability, and undecidability of various problems associated with such machines can be found in [53].…”