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T.A. Henzinger

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5 papers

1 author row

TCS Journal 2002 Journal Article

Axioms for real-time logics

P.-Y. Schobbens
J.-F. Raskin
T.A. Henzinger

This paper presents a complete axiomatization of two decidable propositional real-time linear temporal logics: Event Clock Logic (EventClockTL) and Metric Interval Temporal Logic with past (MetricIntervalTL). The completeness proof consists of an effective proof building procedure for EventClockTL. From this result we obtain a complete axiomatization of MetricIntervalTL by providing axioms translating MetricIntervalTL formulae into EventClockTL formulae, the two logics being equally expressive. Our proof is structured to yield axiomatizations also for interesting fragments of these logics, such as the linear temporal logic of the real numbers (TLR).

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TCS Journal 1995 Journal Article

The algorithmic analysis of hybrid systems

R. Alur
C. Courcoubetis
N. Halbwachs
T.A. Henzinger
P.-H. Ho
X. Nicollin
A. Olivero
J. Sifakis

We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as finite automata equipped with variables that evolve continuously with time according to dynamical laws. For verification purposes, we restrict ourselves to linear hybrid systems, where all variables follow piecewise-linear trajectories. We provide decidability and undecidability results for classes of linear hybrid systems, and we show that standard program-analysis techniques can be adapted to linear hybrid systems. In particular, we consider symbolic model-checking and minimization procedures that are based on the reachability analysis of an infinite state space. The procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space. We also present approximation techniques for dealing with systems for which the iterative procedures do not converge.

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I&C Journal 1994 Journal Article

Symbolic Model Checking for Real-Time Systems

T.A. Henzinger
X. Nicollin
J. Sifakis
S. Yovine

We describe finite-state programs over real-numbered time in a guarded-command language with real-valued clocks or, equivalently, as finite automata with real-valued clocks. Model checking answers the question which states of a real-time program satisfy a branching-time specification (given in an extension of CTL with clock variables). We develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates, without constructing the state space. For this purpose, we introduce a μ-calculus on computation trees over real-numbered time. Unfortunately, many standard program properties, such as response for all nonzeno execution sequences (during which time diverges), cannot be characterized by fixpoints: we show that the expressiveness of the timed μ-calculus is incomparable to the expressiveness of timed CTL. Fortunately, this result does not impair the symbolic verification of "implementable" real-time programs-those whose safety constraints are machine-closed with respect to diverging time and whose fairness constraints are restricted to finite upper bounds on clock values. All timed CTL properties of such programs are shown to be computable as finitely approximable fixpoints in a simple decidable theory.

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I&C Journal 1994 Journal Article

Temporal Proof Methodologies for Timed Transition-Systems

T.A. Henzinger
Z. Manna
A. Pnueli

We extend the specification language of temporal logic, the corresponding verification framework, and the underlying computational model to deal with real-; time properties of reactive systems. The abstract notion of timed transition systems generalizes traditional transition systems conservatively: qualitative fairness requirements are replaced (and superseded) by quantitative lower-bound and upper-bound timing constraints on transitions. This framework can model real-time systems that communicate either through shared variables or by message passing and real-time issues such as timeouts, process priorities (interrupts), and process scheduling. We exhibit two styles for the specification of real-time systems. While the first approach uses time-bounded versions of the temporal operators, the second approach allows explicit references to time through a special clock variable. Corresponding to the two styles of specification, we present and compare two different proof methodologies for the verification of timing requirements that are expressed in these styles. For the bounded-operator style, we provide a set of proof rules for establishing bounded-invariance and bounded-responce properties of timed transition systems. This approach generalizes the standard temporal proof rules for verifying invariance and response properties conservatively. For the explicit-clock style, we exploit the observation that every time-bounded property is a safety property and use the standard temporal proof rules for establishing safety properties.

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I&C Journal 1993 Journal Article

Real-Time Logics: Complexity and Expressiveness

R. Alur
T.A. Henzinger

The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about real-time systems, we combine this classical theory of infinite state sequences with a theory of discrete time, via a monotonic function that maps every state to its time. The resulting theory of timed state sequences is shown to be decidable, albeit nonelementary, and its expressive power is characterized by ω-regular sets. Several more expressive variants are proved to be highly undecidable. This framework allows us to classify a wide variety of real-time logics according to their complexity and expressiveness. Indeed, it follows that most formalisms proposed in the literature cannot be decided. We are, however, able to identify two elementary real-time temporal logics as expressively complete fragments of the theory of timed state sequences, and we present tableau-based decision procedures for checking validity. Consequently, these two formalisms are well-suited for the specification and verification of real-time systems.

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