Minimization for Generalized Boolean Formulas

The minimization problem for propositional formulas is an important optimization problem in the second level of the polynomial hierarchy. In general, the problem is Sigma-2-complete under Turing reductions, but restricted versions are tractable. We study the complexity of minimization for formulas in two established frameworks for restricted propositional logic: The Post framework allowing arbitrarily nested formulas over a set of Boolean connectors, and the constraint setting, allowing generalizations of CNF formulas. In the Post case, we obtain a dichotomy result: Minimization is solvable in polynomial time or coNP-hard. This result also applies to Boolean circuits. For CNF formulas, we obtain new minimization algorithms for a large class of formulas, and give strong evidence that we have covered all polynomial-time cases

New Algebraic Tools for Constraint Satisfaction

The Galois correspondence involving polymorphisms and co-clones has received a lot of attention in regard to constraint satisfaction problems. However, it fails if we are interested in a reduction giving equivalence instead of only satisfiability-equivalence. We show how a similar Galois connection involving weaker closure operators can be applied for these problems. As an example of the usefulness of our construction, we show how to obtain very short proofs of complexity classifications in this context

Deciding Epistemic and Strategic Properties of Cryptographic Protocols

We propose a new, widely applicable model for analyzing knowledge-based (epistemic) and strategic properties of cryptographic protocols. The main result we prove is that the corresponding model checking problem with respect to an expressive epistemic extension of ATL* is decidable. As an application, we prove that abuse-freeness of contract signing protocols is decidable, resolving an open question. Further, we discuss anonymous broadcast and a coin-flipping protoco

Explicit Strategies and Quantification for ATL with Incomplete Information and Probabilistic Games

We introduce QAPI (quantified ATL with probabilism and incomplete information), an extension of ATL that provides a flexible mechanism to reason about strategies that can be identified and followed by agents that do not have complete information about the state of the system. QAPI allows reasoning about strategies directly in the object language, which allows to express complex strategic properties as equilibria. We show how several other logics can be expressed in QAPI, and provide suitable bisimulation relations, as well as complexity and decidability results for the model checking problem

Probabilistic ATL with Incomplete Information

Alternating-time Temporal Logic (ATL) is widely used to reason about strategic abilities of players. Aiming at strategies that can realistically be implemented in software, many variants of ATL study a setting with incomplete information, where strategies may only take available information into account. Another generalization of ATL is Probabilistic ATL, where strategies are required to achieve their goal with a certain probability. We introduce a semantics of ATL that takes into account both of these aspects. We prove that our semantics allows simulation relations similar in spirit to usual bisimulations, and has a decidable model checking problem (in the case of memoryless strategies, with memory-dependent strategies the problem is undecidable)