... Metric Interval Temporal Logic (MITL) as a fragment of the real-time logic Metric Temporal Logic (MTL) in which exact or punctual timing constraints are banned. Their main result showed that model checking and satisfiability for MITL are both EXPSPACE-Complete. Until recently, it was widely believed that admitting even the simplest punctual specifications in any linear-time temporal logic would automatically lead to undecidability. Although this was recently disproved, until now no punctual fragment of MTL was known to have even primitive recursive complexity (with certain decidable fragments having provably non-primitive recursive complexity). In this paper we identify a ‘co-flat ’ subset of MTL that is capable of expressing a large class of punctual specifications and for which model checking (although not satisfiability) has no complexity cost over MITL. Our logic is moreover qualitatively different from MITL in that it can express properties that are not timed-regular. Correspondingly, our decision procedures do not involve translating formulas into finite-state automata, but rather into certain kinds of reversal-bounded Turing machines. Using this translation we show that the model checking problem for our logic is EXPSPACE-Complete

We study complexity issues related to the model-checking problem for LTL with registers (a.k.a. freeze LTL) over one-counter automata. We consider several classes of one-counter automata (mainly deterministic vs. nondeterministic) and several syntactic fragments (restriction on the number of registers and on the use of propositional variables for control locations). The logic has the ability to store a counter value and to test it later against the current counter value. By introducing a non-trivial abstraction on counter values, we show that model checking LTL with registers over deterministic one-counter automata is PSPACEcomplete with infinite accepting runs. By constrast, we prove that model checking LTL with registers over nondeterministic one-counter automata is Σ 1 1-complete [resp. Σ 0 1-complete] in the infinitary [resp. finitary] case even if only one register is used and with no propositional variable. This makes a difference with the facts that several verification problems for one-counter automata are known to be decidable with relatively low complexity, and that finitary satisfiability for LTL with a unique register is decidable. Our results pave the way for model-checking LTL with registers over other classes of operational models, such as reversal-bounded counter machines and deterministic pushdown systems.

Abstract. We introduce PEP, the Post Embedding Problem, a variant of PCP where one compares strings with the subword relation, and PEP reg, a further variant where solutions are constrained and must belong to a given regular language. PEP reg is decidable but not primitive recursive. This entails the decidability of reachability for unidirectional systems with one reliable and one lossy channel. Keywords: Post correspondence problem; Lossy channel systems; Higman’s Lemma. 1

Abstract. We consider the model of priced (a.k.a. weighted) timed automata, an extension of timed automata with cost information on both locations and transitions, and we study various model-checking problems for that model based on extensions of classical temporal logics with cost constraints on modalities. We prove that, under the assumption that the model has only one clock, model-checking this class of models against the logic WCTL, CTL with cost-constrained modalities, is PSPACE-complete (while it has been shown undecidable as soon as the model has three clocks). We also prove that model-checking WMTL, LTL with cost-constrained modalities, is decidable only if there is a single clock in the model and a single stopwatch cost variable (i.e., whose slopes lie in {0, 1}). An interesting direction of real-time model-checking that has recently received substantial attention is the extension and re-targeting of timed automata technology towards optimal scheduling and controller synthesis [AAM06, RLS04, BBL07]. In particular, scheduling problems can often be reformulated in terms of reachability questions with respect to behavioural models where tasks and resources relevant for the scheduling problem in question are modelled as interacting timed automata [BLR05a].

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The basic modal operator bounded until of Metric Temporal Logic (MTL) comes in several variants. In particular it can be strict (when it does not constrain the current instant) or not, and matching (when it requires its two arguments to eventually hold together) or not. This paper compares the relative expressiveness of the resulting MTL variants over dense time. We prove that the expressiveness is not affected by the variations when considering non-Zeno interpretations and arbitrary nesting of temporal operators. On the contrary, the expressiveness changes for flat

Abstract. Whereas formal verification of timed systems has become a very active field of research, the idealised mathematical semantics of timed automata cannot be faithfully implemented. Several works have thus focused on a modified semantics of timed automata which ensures implementability, and robust model-checking algorithms for safety, and later LTL properties have been designed. Recently, a new approach has been proposed, which reduces (standard) model-checking of timed automata to other verification problems on channel machines. Thanks to a new encoding of the modified semantics as a network of timed systems, we propose an original combination of both approaches, and prove that robust model-checking for coFlat-MTL, a large fragment of MTL, is EXPSPACE-Complete. 1

Abstract. We consider asynchronous networks of finite-state systems communicating via a combination of reliable and lossy fifo channels. Depending on the topology, the reachability problem for such networks may be decidable. We provide a complete classification of network topologies according to whether they lead to a decidable reachability problem. Furthermore, this classification can be decided in polynomial-time. 1

Abstract. We consider asynchronous networks of finite-state systems communicating via a combination of reliable and lossy fifo channels. Depending on the topology, the reachability problem for such networks may be decidable. We provide a complete classification of network topologies according to whether they lead to a decidable reachability problem. Furthermore, this classification can be decided in polynomial-time. 1

Abstract. Post’s Embedding Problem is a new variant of Post’s Correspondence Problem where words are compared with embedding rather than equality. It has been shown recently that adding regular constraints on the form of admissible solutions makes the problem highly non-trivial, and relevant to the study of lossy channel systems. Here we consider the infinitary version and its application to recurrent reachability in lossy channel systems. 1