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We study finite automata running over infinite binary trees. A run of such an automaton over an input tree is a tree labeled by control states of the automaton: the labeling is built in a top-down fashion and should be consistent with the transitions of the automaton. A branch in a run is accepting if the ω-word obtained by reading the states along the(More)
We study a model for recursive functional programs called higher order recursion schemes (HORS). We give new proofs of two verification related problems: reflection and selection for HORS. The previous proofs are based on the equivalence between HORS and collapsible pushdown automata and they lose the structure of the initial program. The constructions(More)
Quantitative games are two-player zero-sum games played on directed weighted graphs. Totalpayoff games – that can be seen as a refinement of the well-studied mean-payoff games – are the variant where the payoff of a play is computed as the sum of the weights. Our aim is to describe the first pseudo-polynomial time algorithm for total-payoff games in the(More)
We propose a study of the modes of derivation of higher-order recursion schemes, proving that value trees obtained from schemes using innermost-outermost derivations (IO) are the same as those obtained using unrestricted derivations. Given that higher-order recursion schemes can be used as a model of functional programs, innermost-outermost derivations(More)
We study finite automata running over infinite binary trees and we relax the notion of accepting run by allowing a negligible set (in the sense of measure theory) of non-accepting branches. In this qualitative setting, a tree is accepted by the automaton if there exists a run over this tree in which almost every branch is accepting. This leads to a new(More)
Priced timed games are two-player zero-sum games played on priced timed automata (whose locations and transitions are labeled by weights modeling the costs of spending time in a state and executing an action, respectively). The goals of the players are to minimise and maximise the cost to reach a target location, respectively. We consider priced timed games(More)
The purpose of this work is to investigate the stability property of some models which are currently used in image processing. Following L. Rudin, S.J. Osher and E. Fatemi, we decompose an image f ∈ L2(R2) as a sum u+ v where u belongs to BV(R2) and v belongs to L2(R2). The Banach space BV is aimed at modeling the objects contained in the given image. the(More)
Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games—that can be seen as a refinement of the well-studied mean-payoff games—are the variant where the payoff of a play is computed as the sum of the weights. Our aim is to describe the first pseudo-polynomial time algorithm for total-payoff games in the(More)
We study a generalisation of sabotage games, a model of dynamic network games introduced by van Benthem [16]. The original definition of the game is inherently finite and therefore does not allow one to model infinite processes. We propose an extension of the sabotage games in which the first player (Runner) traverses an arena with dynamic weights(More)
Whereas the second part of the statement concerning the measurability of the set QualAccRuns(A) is correct in full generality, the first part of the statement concerning the measurability of the set QualAccRuns(A) only holds if the automaton A is equipped with a Büchi acceptance condition. This was pointed out to us by Weidner [2014], and we offer warm(More)