Philippe Schnoebelen

Well-structured transition systems everywhere!

Well-structured transition systems (WSTSs) are a general class of infinite-state systems for which decidability results rely on the existence of a well-quasi-ordering between states that is compatible with the transitions. In this article, we provide an extensive treatment of the WSTS idea and show several new results. Our improved definitions allow many examples of classical systems to be seen as instances of WSTSs.

Reset Nets Between Decidability and Undecidability

We study Petri nets with Reset arcs (also Transfer and Doubling arcs) in combination with other extensions of the basic Petri net model. While Reachability is undecidable in all these extensions (indeed they are Turing-powerful), we exhibit unexpected frontiers for the decidability of Termination, Coverability, Boundedness and place-Boundedness. In particular, we show counter-intuitive separations between seemingly related problems. Our main theorem is the very surprising fact that boundedness is undecidable for Petri nets with Reset arcs.

Temporal logic with forgettable past

We investigate NLTL, a linear-time temporal logic with forgettable past. NLTL can be exponentially more succinct than LTL+Past (which in turn can be more succinct than LTL). We study satisfiability and model checking for NLTL and provide optimal automata-theoretic algorithms for these EXPSPACE-complete problems.

Verifying lossy channel systems has nonprimitive recursive complexity

Lossy channel systems are systems of finite state automata that communicate via unreliable unbounded fifo channels. It is known that reachability, termination and a few other verification problems are decidable for these systems. In this article we show that these problems cannot be solved in primitive recursive time.

The complexity of propositional linear temporal logics in simple cases

It is well known that model checking and satisfiability for PLTL are PSPACE-complete. By contrast, very little is known about whether there exist some interesting fragments of PLTL with a lower worst-case complexity. Such results would help understand why PLTL model checkers are successfully used in practice. In this article we investigate this issue and consider model checking and satisfiability for all fragments of PLTL obtainable by restricting (1) the temporal connectives allowed, (2) the number of atomic propositions, and (3) the temporal height. 2002 Elsevier Science (USA).

Towards the automatic verification of PLC programs written in Instruction List

We propose a framework for the automatic verification of PLC (programmable logic controller) programs written in Instruction List, one of the five languages defined in the IEC 61131-3 standard. We propose a formal semantics for a significant fragment of the IL language, and a direct coding of this semantics into a model checking tool. We then automatically verify rich behavioral properties written in linear temporal logic. Our approach is illustrated on the example of the tool-holder of a turning center.

Model Checking Timed Automata with One or Two Clocks

In this paper, we study model checking of timed automata (TAs), and more precisely we aim at finding efficient model checking for subclasses of TAs. For this, we consider model checking TCTL and TCTL ≤,≥ over TAs with one clock or two clocks.

A hierarchy of temporal logics with past

We extend the classical hierarchy of branching-time temporal logics between UB and CTL* by studying which additional expressive power (if any) stems from the incorporation of past-time modalities. In addition, we propose a new temporal combinator, N for “Now”, that brings new and interesting expressive power. In several situations, non-trivial translation algorithms exist from a temporal logic with past to a pure-future fragment. These algorithms have important practical applications e.g. in the field of model-checking.

Revisiting Ackermann-hardness for lossy counter machines and reset Petri nets

We prove that coverability and termination are not primitive-recursive for lossy counter machines and for Reset Petri nets.

Model Checking a Path

We consider the problem of checking whether a finite (or ultimately periodic) run satisfies a temporal logic formula. This problem is at the heart of “runtime verification” but it also appears in many other situations. By considering several extended temporal logics, we show that the problem of model checking a path can usually be solved efficiently, and profit from specialized algorithms. We further show it is possible to efficiently check paths given in compressed form.