### Abstract

We present first the logic MTL, a real-time temporal logic that is at the heart of the real-time specification language ALBERT. Since this logic is undecidable, we approximate it (using the theory of Abstract Interpretation) by its fictitious clock counterpart, MTL^{FC}. We then present a symbolic tableau-based model generation decision procedure in EXPSPACE, which is theoretically optimal. In practice however, we see that the introduction of integer-valued prophecy variables will make it more efficient. From these variables, we reconstruct by reverting the process a logic that we call EXPSPACE, which can be decided in PSPACE, and has the same expressivity as MTL^{FC}. Theory thus shows that memory space is the critical factor. However, the classical compaction of memory space by BDDs is not ideal here, since our integer variables would need to be encoded by booleans. Therefore, we use Sharing Trees instead, a compact data structure that can accommodate arbitrary data types. Preliminary results on this implementation are reported.

Original language | English |
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Pages (from-to) | 113-131 |

Number of pages | 19 |

Journal | Electronic Notes in Theoretical Computer Science |

Volume | 23 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Dec 2001 |

Event | SMC'99, First International Workshop on Symbolic Model Checking (Associated to FLoC'99, the 1999 Federated Logic Conference) - Trento, Italy Duration: 6 Jul 1999 → 6 Jul 1999 |

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*Electronic Notes in Theoretical Computer Science*,

*23*(2), 113-131. https://doi.org/10.1016/S1571-0661(04)80672-8

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*Electronic Notes in Theoretical Computer Science*, vol. 23, no. 2, pp. 113-131. https://doi.org/10.1016/S1571-0661(04)80672-8

**Model-generation of a fictitious clock real-time logic using sharing trees.** / Raskin, Jean François; Schobbens, Pierre Yves; Ferier, Laurent.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Model-generation of a fictitious clock real-time logic using sharing trees

AU - Raskin, Jean François

AU - Schobbens, Pierre Yves

AU - Ferier, Laurent

PY - 2001/12/1

Y1 - 2001/12/1

N2 - We present first the logic MTL, a real-time temporal logic that is at the heart of the real-time specification language ALBERT. Since this logic is undecidable, we approximate it (using the theory of Abstract Interpretation) by its fictitious clock counterpart, MTLFC. We then present a symbolic tableau-based model generation decision procedure in EXPSPACE, which is theoretically optimal. In practice however, we see that the introduction of integer-valued prophecy variables will make it more efficient. From these variables, we reconstruct by reverting the process a logic that we call EXPSPACE, which can be decided in PSPACE, and has the same expressivity as MTLFC. Theory thus shows that memory space is the critical factor. However, the classical compaction of memory space by BDDs is not ideal here, since our integer variables would need to be encoded by booleans. Therefore, we use Sharing Trees instead, a compact data structure that can accommodate arbitrary data types. Preliminary results on this implementation are reported.

AB - We present first the logic MTL, a real-time temporal logic that is at the heart of the real-time specification language ALBERT. Since this logic is undecidable, we approximate it (using the theory of Abstract Interpretation) by its fictitious clock counterpart, MTLFC. We then present a symbolic tableau-based model generation decision procedure in EXPSPACE, which is theoretically optimal. In practice however, we see that the introduction of integer-valued prophecy variables will make it more efficient. From these variables, we reconstruct by reverting the process a logic that we call EXPSPACE, which can be decided in PSPACE, and has the same expressivity as MTLFC. Theory thus shows that memory space is the critical factor. However, the classical compaction of memory space by BDDs is not ideal here, since our integer variables would need to be encoded by booleans. Therefore, we use Sharing Trees instead, a compact data structure that can accommodate arbitrary data types. Preliminary results on this implementation are reported.

UR - http://www.scopus.com/inward/record.url?scp=18944371071&partnerID=8YFLogxK

U2 - 10.1016/S1571-0661(04)80672-8

DO - 10.1016/S1571-0661(04)80672-8

M3 - Conference article

AN - SCOPUS:18944371071

VL - 23

SP - 113

EP - 131

JO - Electronic Notes in Theoretical Computer Science

JF - Electronic Notes in Theoretical Computer Science

SN - 1571-0661

IS - 2

ER -