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The reachability problem for Vector Addition Systems (VASs) is a central problem of net theory. The general problem is known decidable by algorithms exclusively based on the classical Kosaraju-Lambert-Mayr-Sacerdote-Tenney decomposition. This decomposition is used in this paper to prove that the Parikh images of languages accepted by VASs are semi-pseudo-linear; a class that extends the semi-linear...
Model checking is an automatic verification technique for state-transition systems that are finite-state or that have finite-state abstractions. In the early 1980's in a series of joint papers with my graduate students E.A. Emerson and A.P. Sistla, we proposed that model checking could be used for verifying concurrent systems and gave algorithms for this purpose. At roughly the same time, Joseph Sifakis...
The model checking of higher-order recursion schemes has important applications in the verification of higher-order programs. Ong has previously shown that the modal mu-calculus model checking of trees generated by order-n recursion scheme is n-EXPTIME complete, but his algorithm and its correctness proof were rather complex. We give an alternative, type-based verification method: Given a modal mu-calculus...
We exhibit a deterministic concurrent reachability game PURGATORYn with n non-terminal positions and a binary choice for both players in every position so that any positional strategy for Player 1 achieving the value of the game within given isin < 1/2 must use non-zero behavior probabilities that are less than (isin2/(1 - isin))2n-2 . Also, even to achieve the value within say 1 - 2-n/2, doubly...
Graded modal logic is the formal language obtained from ordinary modal logic by endowing its modal operators with cardinality constraints. Under the familiar possible-worlds semantics, these augmented modal operators receive interpretations such as "It is true at no fewer than 15 accessible worlds that ...", or "It is true at no more than 2 accessible worlds that ...". We investigate...
In a constraint satisfaction problem (CSP) the goal is to find an assignment of a given set of variables subject to specified constraints. A global cardinality constraint is an additional requirement that prescribes how many variables must be assigned a certain value. We study the complexity of the problem CCSP(Gamma), the constraint satisfaction problem with global cardinality constraints that allows...
In modal logics, graded (world) modalities have been deeply investigated as a useful framework for generalizing standard existential and universal modalities in such a way that they can express statements about a given number of immediately accessible worlds. These modalities have been recently investigated with respect to the mu-calculus, which have provided succinctness, without affecting the satisfiability...
We study the complexity of the propositional minimal inference problem. Its complexity has been extensively studied before because of its fundamental importance in artificial intelligence and nonmonotonic logics. We prove that the complexity of the minimal inference problem with unbounded queries has a trichotomy (between P, coNP-complete, and Pi2P-complete). This result finally settles with a positive...
We prove that is possible to extend Girard's Ludics so as to have repetitions (hence exponentials), and still have the results on semantical types which characterize Ludics in the panorama of Game Semantics. The results are obtained by using less structure than in the original paper; this has an interest on its own, and we hope that it will open the way to applying the approach of Ludics to a larger...
We present a compact sequent calculus LKU for classical logic organized around the concept of polarization. Focused sequent calculi for classical logic, intuitionistic logic, and multiplicative-additive linear logic are derived as fragments of LKU by increasing the sensitivity of specialized structural rules to polarity information. We develop a unified, streamlined framework for proving cut-elimination...
We study the complexity of evaluating positive equality-free sentences of first-order (FO) logic over a fixed, finite structure B. This may be seen as a natural generalisation of the non-uniform quantified constraint satisfaction problem QCSP(B). We introduce subjective hyper-endomorphisms and use them in proving a Galois connection that characterises definability in positive equality-free FO. Through...
A rewrite closure is an extension of a term rewrite system with new rules, usually deduced by transitivity. Rewrite closures have the nice property that all rewrite derivations can be transformed into derivations of a simple form. This property has been useful for proving decidability results in term rewriting. Unfortunately, when the term rewrite system is not linear, the construction of a rewrite...
After informally reviewing the main concepts from game semantics and placing the development of the field in a historical context we examine its main applications. We focus in particular on finite state model checking, higher order model checking and more recent developments in hardware design.
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages L that assign to each word w a real number L(w). In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit average, or discounted sum of the transition weights. We study expressiveness and closure questions about these quantitative...
Pointer programs are a model of structured computation within LOGSPACE. They capture the common description of LOGSPACE algorithms as programs that take as input some structured data (e.g. a graph) and that store in memory only a constant number of pointers to the input (e.g. to the graph nodes). In this paper we study undirected s-t-reachability for a class of pure pointer programs in which one can...
In this paper we introduce "clipping,'' a new method of syntactic approximation which is motivated by and works in conjunction with a sound and decidable denotational model for a given programming language. Like slicing, clipping reduces the size of the source code in preparation for automatic verification; but unlike slicing it is an imprecise but computationally inexpensive algorithm which...
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order prepositional logic. One of the main difficulties that has to be faced during the elaboration of this kind of semantics is to characterize definable strategies, that is...
Automata on infinite words (omega-automata) have wide applications in formal language theory as well as in modeling and verifying reactive systems. Complementation of omega-automata is a crucial instrument in many these applications, and hence there have been great interests in determining the state complexity of the complementation problem. However, obtaining nontrivial lower bounds has been difficult...
In physics, Feynman diagrams are used to reason about quantum processes. Similar diagrams can also be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of topological quantum field theory and quantum computation, it became clear that diagrammatic reasoning takes advantage of an extensive network of interlocking analogies between...
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