On the decidability and complexity of Metric Temporal Logic over finite words

Metric Temporal Logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also consider the model-checking problem for MTL: whether all words accepted by a given Alur-Dill timed automaton satisfy a given MTL formula. We show that this problem is decidable over finite words. Over infinite words, we show that model checking the safety fragment of MTL--which includes invariance and time-bounded response properties--is also decidable. These results are quite surprising in that they contradict various claims to the contrary that have appeared in the literature

Complexity Hierarchies Beyond Elementary

We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary complexity, which occur naturally in logic, combinatorics, formal languages, verification, etc., with complexities ranging from simple towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep updating the catalogue of problems from Section 6 in future revision

The Parametric Ordinal-Recursive Complexity of Post Embedding Problems

Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page

About Decisiveness of Dynamic Probabilistic Models

Decisiveness of infinite Markov chains with respect to some (finite or infinite) target set of states is a key property that allows to compute the reachability probability of this set up to an arbitrary precision. Most of the existing works assume constant weights for defining the probability of a transition in the considered models. However numerous probabilistic modelings require the (dynamic) weight to also depend on the current state. So we introduce a dynamic probabilistic version of counter machine (pCM). After establishing that decisiveness is undecidable for pCMs even with constant weights, we study the decidability of decisiveness for subclasses of pCM. We show that, without restrictions on dynamic weights, decisiveness is undecidable with a single state and single counter pCM. On the contrary with polynomial weights, decisiveness becomes decidable for single counter pCMs under mild conditions. Then we show that decisiveness of probabilistic Petri nets (pPNs) with polynomial weights is undecidable even when the target set is upward-closed unlike the case of constant weights. Finally we prove that the standard subclass of pPNs with a regular language is decisive with respect to a finite set whatever the kind of weights

Decidability in the logic of subsequences and supersequences

We consider first-order logics of sequences ordered by the subsequence ordering, aka sequence embedding. We show that the \Sigma_2 theory is undecidable, answering a question left open by Kuske. Regarding fragments with a bounded number of variables, we show that the FO2 theory is decidable while the FO3 theory is undecidable

NASA Formal Methods Workshop, 1990

The workshop brought together researchers involved in the NASA formal methods research effort for detailed technical interchange and provided a mechanism for interaction with representatives from the FAA and the aerospace industry. The workshop also included speakers from industry to debrief the formal methods researchers on the current state of practice in flight critical system design, verification, and certification. The goals were: define and characterize the verification problem for ultra-reliable life critical flight control systems and the current state of practice in industry today; determine the proper role of formal methods in addressing these problems, and assess the state of the art and recent progress toward applying formal methods to this area

Modelling and detection of faults in axial-flux permanent magnet machines

The development of various topologies and configurations of axial-flux permanent magnet machine has spurred its use for electromechanical energy conversion in several applications. As it becomes increasingly deployed, effective condition monitoring built on reliable and accurate fault detection techniques is needed to ensure its engineering integrity. Unlike induction machine which has been rigorously investigated for faults, axial-flux permanent magnet machine has not. Thus in this thesis, axial-flux permanent magnet machine is investigated under faulty conditions. Common faults associated with it namely; static eccentricity and interturn short circuit are modelled, and detection techniques are established. The modelling forms a basis for; developing a platform for precise fault replication on a developed experimental test-rig, predicting and analysing fault signatures using both finite element analysis and experimental analysis. In the detection, the motor current signature analysis, vibration analysis and electrical impedance spectroscopy are applied. Attention is paid to fault-feature extraction and fault discrimination. Using both frequency and time-frequency techniques, features are tracked in the line current under steady-state and transient conditions respectively. Results obtained provide rich information on the pattern of fault harmonics. Parametric spectral estimation is also explored as an alternative to the Fourier transform in the steady-state analysis of faulty conditions. It is found to be as effective as the Fourier transform and more amenable to short signal-measurement duration. Vibration analysis is applied in the detection of eccentricities; its efficacy in fault detection is hinged on proper determination of vibratory frequencies and quantification of corresponding tones. This is achieved using analytical formulations and signal processing techniques. Furthermore, the developed fault model is used to assess the influence of cogging torque minimization techniques and rotor topologies in axial-flux permanent magnet machine on current signal in the presence of static eccentricity. The double-sided topology is found to be tolerant to the presence of static eccentricity unlike the single-sided topology due to the opposing effect of the resulting asymmetrical properties of the airgap. The cogging torque minimization techniques do not impair on the established fault detection technique in the single-sided topology. By applying electrical broadband impedance spectroscopy, interturn faults are diagnosed; a high frequency winding model is developed to analyse the impedance-frequency response obtained

EOS: A project to investigate the design and construction of real-time distributed embedded operating systems

The EOS project is investigating the design and construction of a family of real-time distributed embedded operating systems for reliable, distributed aerospace applications. Using the real-time programming techniques developed in co-operation with NASA in earlier research, the project staff is building a kernel for a multiple processor networked system. The first six months of the grant included a study of scheduling in an object-oriented system, the design philosophy of the kernel, and the architectural overview of the operating system. In this report, the operating system and kernel concepts are described. An environment for the experiments has been built and several of the key concepts of the system have been prototyped. The kernel and operating system is intended to support future experimental studies in multiprocessing, load-balancing, routing, software fault-tolerance, distributed data base design, and real-time processing

Model-checking Timed Temporal Logics

AbstractIn this paper, we present several timed extensions of temporal logics, that can be used for model-checking real-time systems. We give different formalisms and the corresponding decidability/complexity results. We also give intuition to explain these results

Alternating register automata on finite words and trees

We study alternating register automata on data words and data trees in relation to logics. A data word (resp. data tree) is a word (resp. tree) whose every position carries a label from a finite alphabet and a data value from an infinite domain. We investigate one-way automata with alternating control over data words or trees, with one register for storing data and comparing them for equality. This is a continuation of the study started by Demri, Lazic and Jurdzinski. From the standpoint of register automata models, this work aims at two objectives: (1) simplifying the existent decidability proofs for the emptiness problem for alternating register automata; and (2) exhibiting decidable extensions for these models. From the logical perspective, we show that (a) in the case of data words, satisfiability of LTL with one register and quantification over data values is decidable; and (b) the satisfiability problem for the so-called forward fragment of XPath on XML documents is decidable, even in the presence of DTDs and even of key constraints. The decidability is obtained through a reduction to the automata model introduced. This fragment contains the child, descendant, next-sibling and following-sibling axes, as well as data equality and inequality tests