Abstract
In previous works, the timed logic TCTL was extended with importants modalities, in order to abstract transient states that last for less than k time units. For all modalities of this extension, called TCTL?, the decidability of the model-checking problem has been proved with an appropriate extension of Alur and Dill’s region graph. But this theoretical result does not support a natural implementation due to its state-space explosion problem. This is not surprising since, even for TCTL timed logics, the model checking algorithm that is implemented in tools like UPPAAL or KRONOS is based on a so-called zone algorithm and data structures like DBMs, rather than on explicit sets of regions. In this paper, we propose a symbolic model-checking algorithm which computes the characteristic sets of some TCTL? formulae and checks their truth values. This algorithm generalizes the zone algorithm for TCTL timed logics. We also present a complete correctness proof of this algorithm, and we describe its implementation using the DBM data structure.
Highlights
These methods have been extended to real-time verification: systems are modeled with timed automata [6], [7] and timed logics like TCTL [3] are used to express timed specification like “any problem is followed by an alarm within 3 seconds”
The structure of the paper is the following: we first recall the main features of timed automata model and give definitions for the syntax and semantics of TCTLΔ timed logic (Section 2); we present after some known decidability results of the TCTLΔ model-checking (Section 3); we describe the classical zone algorithm for TCTL timed logics (Section 4); we present thereafter our algorithm, we give a complete proof of its correctness (Section 5) and the following section www.ijacsa.thesai.org (IJACSA) International Journal of Advanced Computer Science and Applications, Vol 7, No 5, 2016 is devoted to explain how to implement it using the DBMs (Section 6); we end this paper with some concluding remarks (Section 7)
We proposed a symbolic model-checking algorithm that computes the characteristic sets of some TCTLΔ formulae and checks their truth values
Summary
The structure of the paper is the following: we first recall the main features of timed automata model and give definitions for the syntax and semantics of TCTLΔ timed logic (Section 2); we present after some known decidability results of the TCTLΔ model-checking (Section 3); we describe the classical zone algorithm for TCTL timed logics (Section 4); we present thereafter our algorithm, we give a complete proof of its correctness (Section 5) and the following section www.ijacsa.thesai.org (IJACSA) International Journal of Advanced Computer Science and Applications, Vol 7, No 5, 2016 is devoted to explain how to implement it using the DBMs (Section 6); we end this paper with some concluding remarks (Section 7).
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