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In the context of real-time systems, Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are prominent and widely used extensions of Linear Temporal Logic. In this paper, we examine the possibility of using MTL and TPTL to specify properties about classes of non-monotonic data languages over the natural numbers. Words in this class may… (More)

Recently, we have shown that satisfiability for ECTL * with constraints over Z is decidable using a new technique. This approach reduces the satisfiability problem of ECTL * with constraints over some structure A (or class of structures) to the problem whether A has a certain model theoretic property that we called EHD (for " existence of homomorphisms is… (More)

- Claudia Carapelle, Shiguang Feng, Oliver Fern'andez Gil, Karin Quaas
- 2013

Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are prominent extensions of Linear Temporal Logic to specify properties about data languages. In this paper, we consider the class of data languages of non-monotonic data words over the natural numbers. We prove that, in this setting, TPTL is strictly more expressive than MTL. To this… (More)

- Claudia Carapelle, Shiguang Feng, Oliver Fernández Gil, Karin Quaas
- 2014

Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are prominent extensions of Linear Temporal Logic to specify properties about data languages. In this paper, we consider the class of data languages of non-monotonic data words over the natural numbers. We prove that, in this setting, TPTL is strictly more expressive than MTL. To this… (More)

Precise complexity results are derived for the model checking problems for MTL (metric temporal logic) and TPTL (timed propositional temporal logic) on (in)finite data words and deterministic one-counter machines. Depending on the number of register variables and the encoding of numbers in constraints (unary or binary), the complexity is either P-complete… (More)

This paper concerns Grädel's question asked in 1992: whether all problems which are in PTIME and closed under substructures are definable in second-order HORN logic (SO-HORN). We introduce revisions of SO-HORN and DATALOG by adding first-order universal quantifiers over the second-order atoms in the bodies of HORN clauses and DATALOG rules. We show that… (More)

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