Coarse abstractions make Zeno behaviours difficult to detect

An infinite run of a timed automaton is Zeno if it spans only a finite amount of time. Such runs are considered unfeasible and hence it is important to detect them, or dually, find runs that are non-Zeno. Over the years important improvements have been obtained in checking reachability properties for timed automata. We show that some of these very efficient optimizations make testing for Zeno runs costly. In particular we show NP-completeness for the LU-extrapolation of Behrmann et al. We analyze the source of this complexity in detail and give general conditions on extrapolation operators that guarantee a (low) polynomial complexity of Zenoness checking. We propose a slight weakening of the LU-extrapolation that satisfies these conditions

Why Liveness for Timed Automata Is Hard, and What We Can Do About It

The liveness problem for timed automata asks if a given automaton has a run passing infinitely often through an accepting state. We show that unless P=NP, the liveness problem is more difficult than the reachability problem; more precisely, we exhibit a family of automata for which solving the reachability problem with the standard algorithm is in P but solving the liveness problem is NP-hard. This leads us to revisit the algorithmics for the liveness problem. We propose a notion of a witness for the fact that a timed automaton violates a liveness property. We give an algorithm for computing such a witness and compare it with the existing solutions

Efficient Emptiness Check for Timed B\"uchi Automata (Extended version)

The B\"uchi non-emptiness problem for timed automata refers to deciding if a given automaton has an infinite non-Zeno run satisfying the B\"uchi accepting condition. The standard solution to this problem involves adding an auxiliary clock to take care of the non-Zenoness. In this paper, it is shown that this simple transformation may sometimes result in an exponential blowup. A construction avoiding this blowup is proposed. It is also shown that in many cases, non-Zenoness can be ascertained without extra construction. An on-the-fly algorithm for the non-emptiness problem, using non-Zenoness construction only when required, is proposed. Experiments carried out with a prototype implementation of the algorithm are reported.Comment: Published in the Special Issue on Computer Aided Verification - CAV 2010; Formal Methods in System Design, 201

Deriving real-time action systems with multiple time bands using algebraic reasoning

The verify-while-develop paradigm allows one to incrementally develop programs from their specifications using a series of calculations against the remaining proof obligations. This paper presents a derivation method for real-time systems with realistic constraints on their behaviour. We develop a high-level interval-based logic that provides flexibility in an implementation, yet allows algebraic reasoning over multiple granularities and sampling multiple sensors with delay. The semantics of an action system is given in terms of interval predicates and algebraic operators to unify the logics for an action system and its properties, which in turn simplifies the calculations and derivations

Technical Epistemologies: On the medical reception of Hellenistic philosophy

This thesis examines the transposition of Hellenistic philosophy into the medical sphere, with a focus on the Stoic, Epicurean and Pyrrhonian traditions. The intersection of Hellenistic philosophy and medicine is especially abundant; the Hellenistic philosopher, with his eudaimonic orientation, presents himself as a physician of the soul. The τέλος of the medical art – the production and maintenance of health – served as a practical template for the philosopher’s administrations. As the Hellenistic period fades into the centuries of Roman hegemony, Stoic and Epicurean doctrines find their way into the medical tradition per se via the theories of Athenaeus of Attalia and Asclepiades of Bithynia respectively. However, despite the oft-stated affinity of philosophical and medical objectives, Stoicism and Epicureanism are refashioned as they cross disciplinary boundaries – in the case of Epicureanism, radically so. My thesis is that these adjustments are most intelligibly read as attempts by doctors to signify the capacity of their τέχνη to generate new ideas by disentangling their theories from the philosophies to which they were intellectually indebted. The method by which this is achieved, I will argue, is in large part dependent on the nature of the philosophy at root, the ‘mother-doctrine’. Athenaeus was able, through selective adoption, to delineate a technical epistemology within the greater architecture of Stoic theory; Asclepiades, by contrast, was motivated to adapt the physical system he sought to appropriate. The Pyrrhonists, who interface with the medical sphere via their affiliation with the Empiricist sect in the second century AD, represent an alternative mode of interaction between the philosophical and medical traditions – the alliance of independent, differently oriented sects, the integrity of which, I will propose, depends upon the preservation of that independence. The Pyrrhonian Empiricists grant us further insight into the boundary between philosophy and τέχνη as disciplines in antiquity, a boundary which is also central to understanding the medical adoption/adaptation of Stoicism and Epicureanism

Coarse Abstractions Make Zeno Behaviours Difficult to Detect

International audienceAn infinite run of a timed automaton is Zeno if it spans only a finite amount of time. Such runs are considered unfeasible and hence it is important to detect them, or dually, find runs that are non-Zeno. Over the years important improvements have been obtained in checking reachability properties for timed automata. We show that some of these very efficient optimizations make testing for Zeno runs costly. In particular we show NP-completeness for the LU-extrapolation of Behrmann et al. We analyze the source of this complexity in detail and give general conditions on extrapolation operators that guarantee a (low) polynomial complexity of Zenoness checking. We propose a slight weakening of the LU-extrapolation that satisfies these conditions

Coarse abstractions make Zeno behaviours difficult to detect

An infinite run of a timed automaton is Zeno if it spans only a finite amount of time. Such runs are considered unfeasible and hence it is important to detect them, or dually, find runs that are non-Zeno. Over the years important improvements have been obtained in checking reachability properties for timed automata. We show that some of these very efficient optimizations make testing for Zeno runs costly. In particular we show NP-completeness for the LU-extrapolation of Behrmann et al. We analyze the source of this complexity in detail and give general conditions on extrapolation operators that guarantee a (low) polynomial complexity of Zenoness checking. We propose a slight weakening of the LU-extrapolation that satisfies these conditions