Verification for Timed Automata extended with Unbounded Discrete Data Structures

We study decidability of verification problems for timed automata extended with unbounded discrete data structures. More detailed, we extend timed automata with a pushdown stack. In this way, we obtain a strong model that may for instance be used to model real-time programs with procedure calls. It is long known that the reachability problem for this model is decidable. The goal of this paper is to identify subclasses of timed pushdown automata for which the language inclusion problem and related problems are decidable

MTL-Model Checking of One-Clock Parametric Timed Automata is Undecidable

Parametric timed automata extend timed automata (Alur and Dill, 1991) in that they allow the specification of parametric bounds on the clock values. Since their introduction in 1993 by Alur, Henzinger, and Vardi, it is known that the emptiness problem for parametric timed automata with one clock is decidable, whereas it is undecidable if the automaton uses three or more parametric clocks. The problem is open for parametric timed automata with two parametric clocks. Metric temporal logic, MTL for short, is a widely used specification language for real-time systems. MTL-model checking of timed automata is decidable, no matter how many clocks are used in the timed automaton. In this paper, we prove that MTL-model checking for parametric timed automata is undecidable, even if the automaton uses only one clock and one parameter and is deterministic.Comment: In Proceedings SynCoP 2014, arXiv:1403.784

Synchronizing Data Words for Register Automata

Register automata (RAs) are finite automata extended with a finite set of registers to store and compare data from an infinite domain. We study the concept of synchronizing data words in RAs: does there exist a data word that sends all states of the RA to a single state? For deterministic RAs with k registers (k-DRAs), we prove that inputting data words with 2k+1 distinct data from the infinite data domain is sufficient to synchronize. We show that the synchronization problem for DRAs is in general PSPACE-complete, and it is NLOGSPACE-complete for 1-DRAs. For nondeterministic RAs (NRAs), we show that Ackermann(n) distinct data (where n is the size of the RA) might be necessary to synchronize. The synchronization problem for NRAs is in general undecidable, however, we establish Ackermann-completeness of the problem for 1-NRAs. Another main result is the NEXPTIME-completeness of the length-bounded synchronization problem for NRAs, where a bound on the length of the synchronizing data word, written in binary, is given. A variant of this last construction allows to prove that the length-bounded universality problem for NRAs is co-NEXPTIME-complete

Revisiting Reachability in Timed Automata

We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers and reals. In this paper we give a new and simpler proof of this result, building on the well-known reachability analysis of timed automata involving difference bound matrices. Using this new proof, we give an exponential-space procedure for model checking the reachability fragment of the logic parametric TCTL. Finally we show that the latter problem is NEXPTIME-hard

Path Checking for MTL and TPTL over Data Words

Metric temporal logic (MTL) and timed propositional temporal logic (TPTL) are quantitative extensions of linear temporal logic, which are prominent and widely used in the verification of real-timed systems. It was recently shown that the path checking problem for MTL, when evaluated over finite timed words, is in the parallel complexity class NC. In this paper, we derive precise complexity results for the path-checking problem for MTL and TPTL when evaluated over infinite data words over the non-negative integers. Such words may be seen as the behaviours of one-counter machines. For this setting, we give a complete analysis of the complexity of the path-checking problem depending on the number of register variables and the encoding of constraint numbers (unary or binary). As the two main results, we prove that the path-checking problem for MTL is P-complete, whereas the path-checking problem for TPTL is PSPACE-complete. The results yield the precise complexity of model checking deterministic one-counter machines against formulae of MTL and TPTL

The Containment Problem for Unambiguous Register Automata

We investigate the complexity of the containment problem "Does L(A)subseteq L(B) hold?", where B is an unambiguous register automaton and A is an arbitrary register automaton. We prove that the problem is decidable and give upper bounds on the computational complexity in the general case, and when B is restricted to have a fixed number of registers

Pitfalls and potential of institutional change: Rain-index insurance and the sustainability of rangeland management

Rain-index insurance is strongly advocated in many parts of the developing world to help farmers to cope with climatic risk that prevail in (semi-)arid rangelands due to low and highly uncertain rainfall. We present a modeling analysis of how the availability of rain-index insurance affects the sustainability of rangeland management. We show that a rain-index insurance with frequent payos, i.e. a high strike level, leads to the choice of less sustainable grazing management than without insurance available. However, a rain-index insurance with a low to medium strike level enhances the farmer's well-being while not impairing the sustainability of rangeland management.ecological-economic modeling, weather-index insurance, Namibia, grazing management, risk, sustainability, weather-based derivatives

Kleene-Schützenberger and Büchi Theorems for Weighted Timed Automata

In 1994, Alur and Dill introduced timed automata as a simple mathematical model for modelling the behaviour of real-time systems. In this thesis, we extend timed automata with weights. More detailed, we equip both the states and transitions of a timed automaton with weights taken from an appropriate mathematical structure. The weight of a transition determines the weight for taking this transition, and the weight of a state determines the weight for letting time elapse in this state. Since the weight for staying in a state depends on time, this model, called weighted timed automata, has many interesting applications, for instance, in operations research and scheduling. We give characterizations for the behaviours of weighted timed automata in terms of rational expressions and logical formulas. These formalisms are useful for the specification of real-time systems with continuous resource consumption. We further investigate the relation between the behaviours of weighted timed automata and timed automata. Finally, we present important decidability results for weighted timed automata