Frédéric Maris

Arnaud Lequen, Martin C. Cooper, Frédéric Maris

Determining whether two STRIPS planning instances are isomorphic is the simplest form of comparison between planning instances. It is also a particular case of the problem concerned with finding an isomorphism between a planning instance $P$ and a sub-instance of another instance $P_0$ . One application of such a mapping is to efficiently produce a compiled form containing all solutions to P from a compiled form containing all solutions to $P_0$. We also introduce the notion of embedding from an instance $P$ to another instance $P_0$, which allows us to deduce that $P_0$ has no solution-plan if $P$ is unsolvable. In this paper, we study the complexity of these problems. We show that the first is GI-complete, and can thus be solved, in theory, in quasi-polynomial time. While we prove the remaining problems to be NP-complete, we propose an algorithm to build an isomorphism, when possible. We report extensive experimental trials on benchmark problems which demonstrate conclusively that applying constraint propagation in preprocessing can greatly improve the efficiency of a SAT solver.

Martin C. Cooper, Andreas Herzig, Faustine Maffre et al.

The gossip problem, in which information (known as secrets) must be shared among a certain number of agents using the minimum number of calls, is of interest in the conception of communication networks and protocols. We extend the gossip problem to arbitrary epistemic depths. For example, we may require not only that all agents know all secrets but also that all agents know that all agents know all secrets. We give optimal protocols for various versions of the generalised gossip problem, depending on the graph of communication links, in the case of two-way communications, one-way communications and parallel communication. We also study different variants which allow us to impose negative goals such as that certain agents must not know certain secrets. We show that in the presence of negative goals testing the existence of a successful protocol is NP-complete whereas this is always polynomial-time in the case of purely positive goals.

Khaled Skander Ben Slimane, Alexis Comte, Olivier Gasquet et al.

SAT provers are powerful tools for solving real-sized logic problems, but using them requires solid programming knowledge and may be seen w.r.t.\ logic like assembly language w.r.t.\ programming. Something like a high level language was missing to ease various users to take benefit of these tools. {\sc \texttt {TouIST}}\ aims at filling this gap. It is devoted to propositional logic and its main features are 1) to offer a high-level logic langage for expressing succintly complex formulas (e.g.\ formulas describing Sudoku rules, planification problems,\ldots) and 2) to find models to these formulas by using the adequate powerful prover, which the user has no need to know about. It consists in a friendly interface that offers several syntactic facilities and which is connected with some sufficiently powerful provers allowing to automatically solve big instances of difficult problems (such as time-tables or Sudokus). It can interact with various provers: pure SAT solver but also SMT provers (SAT modulo theories - like linear theory of reals, etc) and thus may also be used by beginners for experiencing with pure propositional problems up to graduate students or even researchers for solving planification problems involving big sets of fluents and numerical constraints on them.