No abstract

We propose a tableau-based decision procedure for the full Alternating-time Temporal Logic ATL * . We extend our procedure for ATL + in order to deal with nesting of temporal operators. As a side effect, we obtain a new and conceptually simple tableau method for CTL * . The worst case complexity of our procedure is 3EXPTIME, which is suboptimal compared to the 2EXPTIME complexity of the problem. However our method is human-readable and easily implementable. A web application and binaries for our procedure are available at http:// atila.ibisc.univ-evry.fr/tableau ATL star/.

We develop a sound, complete, and practically implementable tableau-based decision method for constructive satisfiability testing and model synthesis for the fragment ATL + of the full alternating-time temporal logic ATL * . The method extends in an essential way a previously developed tableau-based decision method for ATL and works in 2EXPTIME, which is the optimal worst-case complexity of the satisfiability problem for ATL + . We also discuss how suitable parameterizations and syntactic restrictions on the class of input ATL + formulas can reduce the complexity of the satisfiability problem.

We develop a sound, complete and practically implementable tableaubased decision method for constructive satisfiability testing and model synthesis for the fragment ATL + of the full Alternating time temporal logic ATL * . The method extends in an essential way a previously developed tableau-based decision method for ATL and works in 2EXPTIME, which is the optimal worst-case complexity of the satisfiability problem for ATL + . We also discuss how suitable parameterizations and syntactic restrictions on the class of input ATL + formulae can reduce the complexity of the satisfiability problem.