A Metric for Linear Temporal Logic

We propose a measure and a metric on the sets of infinite traces generated by a set of atomic propositions. To compute these quantities, we first map properties to subsets of the real numbers and then take the Lebesgue measure of the resulting sets. We analyze how this measure is computed for Linear Temporal Logic (LTL) formulas. An implementation for computing the measure of bounded LTL properties is provided and explained. This implementation leverages SAT model counting and effects independence checks on subexpressions to compute the measure and metric compositionally

Analytic Torsion of Z_2-graded Elliptic Complexes

We define analytic torsion of Z_2-graded elliptic complexes as an element in the graded determinant line of the cohomology of the complex, generalizing most of the variants of Ray-Singer analytic torsion in the literature. It applies to a myriad of new examples, including flat superconnection complexes, twisted analytic and twisted holomorphic torsions, etc. The definition uses pseudo-differential operators and residue traces. We also study properties of analytic torsion for Z_2-graded elliptic complexes, including the behavior under variation of the metric. For compact odd dimensional manifolds, the analytic torsion is independent of the metric, whereas for even dimensional manifolds, a relative version of the analytic torsion is independent of the metric. Finally, the relation to topological field theories is studied.Comment: 14 pages, typos corrected and other minor changes made in the revised versio

An Efficient Algorithm for Monitoring Practical TPTL Specifications

We provide a dynamic programming algorithm for the monitoring of a fragment of Timed Propositional Temporal Logic (TPTL) specifications. This fragment of TPTL, which is more expressive than Metric Temporal Logic, is characterized by independent time variables which enable the elicitation of complex real-time requirements. For this fragment, we provide an efficient polynomial time algorithm for off-line monitoring of finite traces. Finally, we provide experimental results on a prototype implementation of our tool in order to demonstrate the feasibility of using our tool in practical applications

On-Line Monitoring for Temporal Logic Robustness

In this paper, we provide a Dynamic Programming algorithm for on-line monitoring of the state robustness of Metric Temporal Logic specifications with past time operators. We compute the robustness of MTL with unbounded past and bounded future temporal operators MTL over sampled traces of Cyber-Physical Systems. We implemented our tool in Matlab as a Simulink block that can be used in any Simulink model. We experimentally demonstrate that the overhead of the MTL robustness monitoring is acceptable for certain classes of practical specifications

Tensor-Based Link Prediction in Intermittently Connected Wireless Networks

Through several studies, it has been highlighted that mobility patterns in mobile networks are driven by human behaviors. This effect has been particularly observed in intermittently connected networks like DTN (Delay Tolerant Networks). Given that common social intentions generate similar human behavior, it is relevant to exploit this knowledge in the network protocols design, e.g. to identify the closeness degree between two nodes. In this paper, we propose a temporal link prediction technique for DTN which quantifies the behavior similarity between each pair of nodes and makes use of it to predict future links. Our prediction method keeps track of the spatio-temporal aspects of nodes behaviors organized as a third-order tensor that aims to records the evolution of the network topology. After collapsing the tensor information, we compute the degree of similarity for each pair of nodes using the Katz measure. This metric gives us an indication on the link occurrence between two nodes relying on their closeness. We show the efficiency of this method by applying it on three mobility traces: two real traces and one synthetic trace. Through several simulations, we demonstrate the effectiveness of the technique regarding another approach based on a similarity metric used in DTN. The validity of this method is proven when the computation of score is made in a distributed way (i.e. with local information). We attest that the tensor-based technique is effective for temporal link prediction applied to the intermittently connected networks. Furthermore, we think that this technique can go beyond the realm of DTN and we believe this can be further applied on every case of figure in which there is a need to derive the underlying social structure of a network of mobile users.Comment: 13 pages, 9 figures, 8 tables, submitted to the International Journal of Computer and Telecommunications Networking (COMNET