We consider parity games, a special form of two-player infiniteduration games on numerically labelled graphs, whose winning condition requires that the maximal value of a label occurring infinitely often during a play be of some specific parity. The problem has a rather intriguing status from a complexity theoretic viewpoint, since it belongs to the class UPTime ∩ CoUPTime, and still open is the question whether it can be solved in polynomial time. Parity games also have great practical interest, as they arise in many fields of theoretical computer science, most notably logic, automata theory, and formal verification. In this paper, we propose a new algorithm for the solution of the problem, based on the idea of promoting vertices to higher priorities during the search for winning regions. The proposed approach has nice computational properties, exhibiting the best space complexity among the currently known solutions. Experimental results on both random games and benchmark families show that the technique is also very effective in practice.

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We consider parity games, a special form of two-player infiniteduration games on numerically labelled graphs, whose winning condition requires that the maximal value of a label occurring infinitely often during a play be of some specific parity. The problem has a rather intriguing status from a complexity theoretic viewpoint, since it belongs to the class UPTime ∩ CoUPTime, and still open is the question whether it can be solved in polynomial time. Parity games also have great practical interest, as they arise in many fields of theoretical computer science, most notably logic, automata theory, and formal verification. In this paper, we propose a new algorithm for the solution of the problem, based on the idea of promoting vertices to higher priorities during the search for winning regions. The proposed approach has nice computational properties, exhibiting the best space complexity among the currently known solutions. Experimental results on both random games and benchmark families show that the technique is also very effective in practice.

Abstract. In previous work we presented a model checking procedure for linear programs, i.e. programs in which variables range over a numeric domain and expressions involve linear combinations of the variables. In this paper we lift our model checking procedure for linear programs to deal with arrays via iterative abstraction refinement. While most approaches are based on predicate abstraction and therefore the abstraction is relative to sets of predicates, in our approach the abstraction is relative to sets of variables and array indexes, and the abstract program can express complex correlations between program variables and array elements. Thus, while arrays are problematic for most of the approaches based on predicate abstraction, our approach treats them in a precise way. This is an important feature as arrays are ubiquitous in programming. We provide a detailed account of both the abstraction and the refinement processes, discuss their implementation in the eureka tool, and present experimental results that confirm the effectiveness of our approach on a number of programs of interest.

One of the key challenges in the development of open semantic-based systems is enabling the exchange of meaningful information across applications which may use autonomously developed schemata. One of the typical solutions for that problem is the definition of a mapping between pairs of schemas, namely a set of point-to-point relations between the elements of different schemas. A lot of (semi-)automatic methods for generating such mappings have been proposed. In this paper we provide a preliminary investigation on the notion of correctness for schema matching methods. In particular we define different notions of soundness, strictly depending on what dimension (syntactic, semantic, pragmatic) of the language the mappings are defined on. Finally, we discuss some preliminary conditions under which a two different notions of soundness (semantic and pragmatic) can be related.

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Parity games are two-player infinite-duration games on graphs that play a crucial role in various fields of theoretical computer science. Finding efficient algorithms to solve these games in practice is widely acknowledged as a core problem in formal verification, as it leads to efficient solutions of the model-checking and satisfiability problems of expressive temporal logics, e.g., the modal μCalculus. Their solution can be reduced to the problem of identifying sets of positions of the game, called dominions, in each of which a player can force a win by remaining in the set forever. Recently, a novel technique to compute dominions, called priority promotion, has been proposed, which is based on the notions of quasi dominion, a relaxed form of dominion, and dominion space. The underlying framework is general enough to accommodate different instantiations of the solution procedure, whose correctness is ensured by the nature of the space itself. In this paper we propose a new such instantiation, called region recovery, that tries to reduce the possible exponential behaviours exhibited by the original method in the worst case. The resulting procedure not only often outperforms the original priority promotion approach, but so far no exponential worst case is known