Specifications for reactive systems often consist of environment assumptions and system guarantees. An implementation should not only be correct, but also robust in the sense that it behaves reasonably even when the assumptions are (temporarily) violated. We present an extension of the requirements analysis and synthesis tool RATSY that is able to synthesize robust systems from GR(1) specificat...

Reactive systems are often modelled as two person antagonistic games where one player represents the system while his adversary represents the environment. Undoubtedly, the most popular games in this context are parity games and their cousins (Rabin, Streett and Muller games). Recently however also games with other types of payments, like discounted or mean-payoff [5,6], previously used only in...

We introduce weighted automata over infinite words with Muller acceptance condition and we show that their behaviors coincide with the semantics of weighted restricted MSOsentences. Furthermore, we establish an equivalence property of weighted Muller and weighted Büchi automata over certain semirings. DOI: 10.3103/S1066369X10010044

We determine the complexity of topological properties (i.e., properties closed under the Wadge equivalence) of regular ω-languages by showing that they are typically NL-complete (PSPACEcomplete) for the deterministic Muller, Mostowski and Büchi automata (respectively, for the nondeterministic Rabin, Muller, Mostowski and Büchi automata). For the deterministic Rabin and Streett automata and for ...

We describe a tool that inputs a deterministic ω-automaton with any acceptance condition, and synthesizes an equivalent ω-automaton with another arbitrary acceptance condition and a given number of states, if such an automaton exists. This tool, that relies on a SAT-based encoding of the problem, can be used to provide minimal ω-automata equivalent to given properties, for different acceptance ...

Zero automata are a probabilistic extension of parity automata on infinite trees. The satisfiability of a certain probabilistic variant of mso, called tmso + zero, reduces to the emptiness problem for zero automata. We introduce a variant of zero automata called nonzero automata. We prove that for every zero automaton there is an equivalent nonzero automaton of quadratic size and the emptiness ...

In this paper, ω-closed sets and ω-open sets are used to define and investigate a new class of functions. Relationships between this new class and other classes of functions are established.

This paper concerns rigidity results to Serrin’s overdetermined problem in an epigraph  ∆u + f(u) = 0, in Ω = {(x′, xn) : xn > φ(x′)}, u > 0, in Ω, u = 0, on ∂Ω, |∇u| = const., on ∂Ω. We prove that up to isometry the epigraph must be an half space and that the solution u must be one-dimensional, provided that one of the following assumptions are satisfied: either n = 2; or φ is globally ...