Permutation Games for the Weakly Aconjunctive μ\mu-Calculus

We introduce a natural notion of limit-deterministic parity automata and present a method that uses such automata to construct satisfiability games for the weakly aconjunctive fragment of the $\mu$-calculus. To this end we devise a method that determinizes limit-deterministic parity automata of size $n$ with $k$ priorities through limit-deterministic B\"uchi automata to deterministic parity automata of size $\mathcal{O}((nk)!)$ and with $\mathcal{O}(nk)$ priorities. The construction relies on limit-determinism to avoid the full complexity of the Safra/Piterman-construction by using partial permutations of states in place of Safra-Trees. By showing that limit-deterministic parity automata can be used to recognize unsuccessful branches in pre-tableaux for the weakly aconjunctive $\mu$-calculus, we obtain satisfiability games of size $\mathcal{O}((nk)!)$ with $\mathcal{O}(nk)$ priorities for weakly aconjunctive input formulas of size $n$ and alternation-depth $k$. A prototypical implementation that employs a tableau-based global caching algorithm to solve these games on-the-fly shows promising initial results

Exploiting the Temporal Logic Hierarchy and the Non-Confluence Property for Efficient LTL Synthesis

The classic approaches to synthesize a reactive system from a linear temporal logic (LTL) specification first translate the given LTL formula to an equivalent omega-automaton and then compute a winning strategy for the corresponding omega-regular game. To this end, the obtained omega-automata have to be (pseudo)-determinized where typically a variant of Safra's determinization procedure is used. In this paper, we show that this determinization step can be significantly improved for tool implementations by replacing Safra's determinization by simpler determinization procedures. In particular, we exploit (1) the temporal logic hierarchy that corresponds to the well-known automata hierarchy consisting of safety, liveness, Buechi, and co-Buechi automata as well as their boolean closures, (2) the non-confluence property of omega-automata that result from certain translations of LTL formulas, and (3) symbolic implementations of determinization procedures for the Rabin-Scott and the Miyano-Hayashi breakpoint construction. In particular, we present convincing experimental results that demonstrate the practical applicability of our new synthesis procedure

Traditional Wisdom and Monte Carlo Tree Search Face-to-Face in the Card Game Scopone

We present the design of a competitive artificial intelligence for Scopone, a popular Italian card game. We compare rule-based players using the most established strategies (one for beginners and two for advanced players) against players using Monte Carlo Tree Search (MCTS) and Information Set Monte Carlo Tree Search (ISMCTS) with different reward functions and simulation strategies. MCTS requires complete information about the game state and thus implements a cheating player while ISMCTS can deal with incomplete information and thus implements a fair player. Our results show that, as expected, the cheating MCTS outperforms all the other strategies; ISMCTS is stronger than all the rule-based players implementing well-known and most advanced strategies and it also turns out to be a challenging opponent for human players.Comment: Preprint. Accepted for publication in the IEEE Transaction on Game

Non-Zero Sum Games for Reactive Synthesis

In this invited contribution, we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications. These solution concepts are developed in the context of non-zero sum games played on graphs. They are part of the contributions obtained in the inVEST project funded by the European Research Council.Comment: LATA'16 invited pape