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We study data nets, a generalisation of Petri nets in which tokens carry data from linearly-ordered infinite domains and in which whole-place operations such as resets and transfers are possible. Data nets subsume several known classes of infinite-state systems, including multiset rewriting systems and polymorphic systems with arrays. We show that… (More)

We present a framework for model checking concurrent software systems which incorporates both states and events. Contrary to other state/event approaches, our work also integrates two powerful verification techniques, counterexample-guided abstraction refinement and compositional reasoning. Our specification language is a state/event extension of linear… (More)

- Joël Ouaknine, James Worrell
- 20th Annual IEEE Symposium on Logic in Computer…
- 2005

Metric temporal logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also consider the model-checking problem for MTL: whether all words accepted by a given Alur-Dill timed automaton satisfy a… (More)

- Joël Ouaknine
- FCT
- 2012

Linear recurrence sequences (LRS), such as the Fibonacci numbers, permeate vast areas of mathematics and computer science. In this talk, we consider three natural decision problems for LRS, namely the Skolem Problem (does a given LRS have a zero?), the Positivity Problem (are all terms of a given LRS positive?), and the Ultimate Positivity Problem (are all… (More)

- Joël Ouaknine, James Worrell
- Logical Methods in Computer Science
- 2007

Metric Temporal Logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also consider the model-checking problem for MTL: whether all words accepted by a given Alur-Dill timed automaton satisfy a… (More)

- Joël Ouaknine, James Worrell
- TACAS
- 2006

Metric Temporal Logic (MTL) is a widely-studied real-time extension of Linear Temporal Logic. In this paper we consider a fragment of MTL, called Safety MTL, capable of expressing properties such as invariance and time-bounded response. Our main result is that the satisfiability problem for Safety MTL is decidable. This is the first positive decidability… (More)

- Björn Wachter, Daniel Kroening, Joël Ouaknine
- FMCAD
- 2013

—Lazy abstraction with interpolants, also known as the Impact algorithm, is en vogue as a state-of-the-art software model-checking technique for sequential programs. However, a direct extension of the Impact algorithm to concurrent programs is bound to be inefficient as it has to explore all thread interleavings, which leads to control-state explosion. To… (More)

We present a new decision procedure for finite-precision bit-vector arithmetic with arbitrary bit-vector operations. Our procedure alternates between generating under-and over-approximations of the original bit-vector formula. An under-approximation is obtained by a translation to propositional logic in which some bit-vector variables are encoded with fewer… (More)

- Joël Ouaknine, James Worrell
- FORMATS
- 2008

Metric Temporal Logic (MTL) is a widely-studied real-time extension of Linear Temporal Logic. In this paper we survey results about the complexity of the satisfiability and model checking problems for fragments of MTL with respect to different semantic models. We show that these fragments have widely differing complexities: from polynomial space to… (More)

- Inês Lynce, Joël Ouaknine
- ISAIM
- 2006

Sudoku is a very simple and well-known puzzle that has achieved international popularity in the recent past. This paper addresses the problem of encoding Sudoku puzzles into conjunc-tive normal form (CNF), and subsequently solving them using polynomial-time propositional satisfiability (SAT) inference techniques. We introduce two straightforward SAT… (More)