2,763 research outputs found
Model Checking the Quantitative mu-Calculus on Linear Hybrid Systems
We study the model-checking problem for a quantitative extension of the modal
mu-calculus on a class of hybrid systems. Qualitative model checking has been
proved decidable and implemented for several classes of systems, but this is
not the case for quantitative questions that arise naturally in this context.
Recently, quantitative formalisms that subsume classical temporal logics and
allow the measurement of interesting quantitative phenomena were introduced. We
show how a powerful quantitative logic, the quantitative mu-calculus, can be
model checked with arbitrary precision on initialised linear hybrid systems. To
this end, we develop new techniques for the discretisation of continuous state
spaces based on a special class of strategies in model-checking games and
present a reduction to a class of counter parity games.Comment: LMCS submissio
Internal Calculi for Separation Logics
We present a general approach to axiomatise separation logics with heaplet semantics with no external features such as nominals/labels. To start with, we design the first (internal) Hilbert-style axiomatisation for the quantifier-free separation logic SL(?, -*). We instantiate the method by introducing a new separation logic with essential features: it is equipped with the separating conjunction, the predicate ls, and a natural guarded form of first-order quantification. We apply our approach for its axiomatisation. As a by-product of our method, we also establish the exact expressive power of this new logic and we show PSpace-completeness of its satisfiability problem
Synthesising Strategy Improvement and Recursive Algorithms for Solving 2.5 Player Parity Games
2.5 player parity games combine the challenges posed by 2.5 player
reachability games and the qualitative analysis of parity games. These two
types of problems are best approached with different types of algorithms:
strategy improvement algorithms for 2.5 player reachability games and recursive
algorithms for the qualitative analysis of parity games. We present a method
that - in contrast to existing techniques - tackles both aspects with the best
suited approach and works exclusively on the 2.5 player game itself. The
resulting technique is powerful enough to handle games with several million
states
Abstraction and probabilities for hybrid logics
We suggest and develop mathematical foundations for quantitative versions of hybrid logics by means of two related themes: a relational abstraction technique for hybrid computation tree logic and hybrid Kripke structures as an extension of the model-checking framework for computation tree logic with the ability to name, bind, and retrieve states; and a syntax and semantics for hybrid probabilistic computation tree logic over hybrid extensions of labelled Markov chains for which the relational abstraction techniques of hybrid Kripke structures should be transferable
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