Efficient model checking of the stochastic logic CSLTA

Abstract

CSL TA is a stochastic temporal logic for continuous-time Markov chains (CTMCs), which includes the more known CSL. CSL TA properties are defined through single-clock Deterministic Timed Automata (DTAs). The model checking of CSL TA amounts, in the worst-case, to the computation of the steady-state probability of a non-ergodic Markov Regenerative Process (MRgP) in the size of |CTMC|×|DTA|. Various MRgP solution techniques are available in the literature, and we shall use the Component Method, that computes the steady state distribution of a non-ergodic MRgP by recognizing that, in a MRgP, certain components may actually be solved at a lower cost (same cost as that of a CTMC solution). Unfortunately the technique still requires the construction of the whole MRgP. This paper applies the Component Method to devise various CSL TA model checking algorithms, forward and backward. The Component Method can be applied to the MRgP constructed from the CTMC and the DTA, which is a rather straightforward application of the method, or to the MRgP constructed from the CTMC and the region graph of the DTA, a construction that accounts for timed reachability in the DTA and that allows, in most cases, a significant reduction in the considered MRgP states. In both cases the whole MRgP is built. The primary result of this paper is instead to devise a model-checking algorithm in which the component identification is based only on the region graph of the DTA. The MRgP components are generated "on-the-fly", when needed, starting from the components of the region graph; they are then solved with the cheapest available solution method. Once a component has been solved it is discarded, therefore the whole MRgP is never constructed nor solved. The on-the-fly algorithm is "adaptive": the time and space depend on the formula, and, when the DTA actually expresses a CSL property, the algorithm reduces, seaming-less, to that of standard CSL model checking algorithms.

Expressiveness and Conciseness of Timed Automata for the Verification of Stochastic Models

“…We plan to investigate whether the precise identification of the characteristics that enhance expressiveness and conciseness can help the identification of the best algorithms for CSL TA model-checking, in particular for the componentbased method [4]. Moreover, following the suggestion by an anonymous reviewer, we intend to investigate further consequences of Proposition 1, for example to study systems that include probabilistic choices of autonomous transitions.…”

“…In this paper we concentrate on single-clock CSL TA with autonomous transitions, as in the original definition of CSL TA . Indeed the single-clock limitation is a necessary requirement to reduce the CSL TA model-checking problem to the (steady-state) solution of a Markov Regenerative Process, which is the largest class of stochastic processes for which we can compute an exact numerical solution, supported by efficient solution tools [3,4]. The single-clock setting allows also to investigate whether the definition of CSL TA in [10,13], once limited to a single clock, is equivalent to the original definition of CSL TA (introduced in [12]).…”

Guarded Autonomous Transitions Increase Conciseness and Expressiveness of Timed Automata

“…We can also state that CSL TA specifications that include guarded transitions can be more concise than CSL TA that considers guarded locations. Since the number of locations may significantly affect the complexity of model-checking CSL TA , it is future work to investigate how the component-based model-checking of CSL TA [1] can take advantage of the results of this paper to lower the cost of model-checking.…”

“…ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÑ px n , d n y, v n ,x 1 n , δ n q¨¨¨be a run of A 1 . For all k define r k as the original reset that associated with the creation of the transition labelled by γ k`dk´1 , B k , r 1 k . For all k define c k by c 0 " 0 and for k ą 0:…”

How to Bake Quantum into Your Pet Petri Nets and Have Your Net Theory Too

“…Industry-strength model-checkers exist for years capable of handling hundreds of millions of states (cf. e.g., [11,2]), often using special on-the-fly methods for dealing with the 100s of millions of states without storing transition matrices. The semantics of PNs has led to their use as formal models for real-time, distributed and parallel programming languages, for software systems and services.…”