Recently, a hierarchy of spatio-temporal languages based on the propositional temporal logic PTL and the spatial languages RCC-8, BRCC-8 and S4u has been introduced. Although a number of results on their computational properties were obtained, the most important questions were left open.

Constraint LTL, a generalization of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints. The freeze quantifier can be part of the language, as in some real-time logics, but this variable-binding mechanism is quite general and ubiquitous in many logical languages (first-order temporal logics, hybrid logics, logics for sequence diagrams, navigation logics, etc.). We show that Constraint LTL over the simple domain =# augmented with the freeze operator is undecidable which is a surprising result regarding the poor language for constraints (only equality tests). Many versions of freeze-free Constraint LTL are decidable over domains with qualitative predicates and our undecidability result actually establishes # 1 -completeness. On the positive side, we provide complexity results when the domain is finite (EXPSPACE-completeness) or when the formulae are flat in a sense introduced in the paper. Our undecidability results are quite sharp (i.e. with restrictions on the number of variables) and all our complexity characterizations insure completeness with respect to some complexity class (mainly PSPACE and EXPSPACE).

In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic the spatial logics RCC-8, BRCC-8, S4 u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and `computational realisability' within the hierarchy. We demonstrate how di#erent combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete.

Abstract. Periodicity constraints are used in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. In the paper, we introduce the logic PLTL mod, an extension of Linear-Time Temporal Logic LTL with past-time operators whose atomic formulae are defined from a first-order constraint language dealing with periodicity. Although the underlying constraint language is a fragment of Presburger arithmetic shown to admit a pspace-complete satisfiability problem, we establish that PLTL mod model-checking and satisfiability problems remain in pspace as plain LTL (full Presburger LTL is known to be highly undecidable). This is particularly interesting for dealing with periodicity constraints since the language of PLTL mod has a language more concise than existing languages and the temporalization of our first-order language of periodicity constraints has the same worst case complexity as the underlying constraint language. Finally, we show examples of introduction the quantification in the logical language that provide to PLTL mod, expspacecomplete problems. As another application, we establish that the equivalence problem for extended single-string automata, known to express the equality of time granularities, is pspace-complete by designing a reduction from QBF and by using our results for PLTL mod. Key-words: Presburger LTL, periodicity constraints, computational complexity, Büchi automaton, QBF.

Abstract. Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this word-related notion extends to more complex models, such as those developed for modeling distributed or timed behaviors. In the beginning was the Word... Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those developed for modeling distributed or timed behaviors. The notion of recognizable languages is a familiar one, associated with classical theorems by Kleene, Myhill, Nerode, Elgot, Büchi, Schützenberger, etc. It can be approached from several angles: recognizability by automata, recognizability by finite monoids or finite-index congruences, rational expressions, monadic second

This thesis addresses the discretionary privacy demands of users in heterogeneous distributed systems such as ubiquitous computing environments. Because of the physical proximity and pervasiveness of personal devices, sensors, actuators, and other devices and services, ubiquitous computing environments need a powerful infrastructure for coordinating accesses to these resources. However, this infras-tructure makes it easy for malicious administrators to gain access to private infor-mation of users. We present models for privacy of a user’s communication, unlink-ability of a user’s accesses, and authorized policy feedback that is both useful and privacy preserving. Our models expose the potential threats to a user’s privacy, and allow users to express their individual and differing privacy demands based on these threats. We show how a user’s privacy policies can be efficiently satisfied under our models. For secure and private communication, we present a model for trustworthy rout-ing, with a policy specification language that is computationally efficient to en-force. We show how quantitative trust models can be used to find trustworthy paths of communication and explore various semantic models of trust. For the unlinkability of a user’s accesses to services in a ubiquitous computing environ-ment, we present a model based on access control and decentralized enforcement of policy constraints. We prove that our solution is secure, and show how security can be maintained by trading off precision for evolving protection state. Lastly, we present a model called Know for providing feedback regarding access control deci-sions to users. This model aims to make ubiquitous computing environments more usable and secure, while honoring the privacy of other users in the system. Admin-istrators can specify meta-policies to tailor feedback to individual users based on perceived threat to the policy’s contents. iii To my parents Who valued my education Above all else iv

Abstract. Various logical formalisms with the freeze quantifier have been recently considered to model computer systems even though this is a powerful mechanism that often leads to undecidability. In this paper, we study a linear-time temporal logic with past-time operators such that the freeze operator is only used to express that some value from an infinite set is repeated in the future or in the past. Such a restriction has been inspired by a recent work on spatio-temporal logics. We show decidability of finitary and infinitary satisfiability by reduction into the verification of temporal properties in Petri nets. This is a surprising result since the logic is closed under negation, contains future-time and past-time temporal operators and can express the nonce property and its negation. These ingredients are known to lead to undecidability with a more liberal use of the freeze quantifier. 1

Abstract. Recently, LTL extended with atomic formulas built over a constraint language interpreting variables in Z has been shown to have a decidable satisfiability and model-checking problem. This language allows to compare the variables at different states of the model and include periodicity constraints, comparison constraints, and a restricted form of quantification. On the other hand, the CTL counterpart of this logic (and hence also its CTL ∗ counterpart which subsumes both LTL and CTL) has an undecidable model-checking problem. In this paper, we substantially extend the decidability border, by considering a meaningful fragment of CTL ∗ extended with such constraints (which subsumes both the universal and existential fragments, as well as the EF-like fragment) and show that satisfiability and model-checking over relational automata that are abstraction of counter machines are decidable. The correctness and the termination of our algorithm rely on a suitable well quasi-ordering defined over the set of variable valuations. 1

Abstract. We introduce an LTL-like logic with atomic formulae built over a constraint language interpreting variables in Z. The constraint language includes periodicity constraints, comparison constraints of the form x = y and x < y, it is closed under Boolean operations and it admits a restricted form of existential quantification. This is the largest set of qualitative constraints over Z known so far, shown to admit a decidable LTL extension. Such constraints are those used for instance in calendar formalisms or in abstractions of counter automata by using congruences modulo some power of two. Indeed, various programming languages perform arithmetic operators modulo some integer. We show that the satisfiability and model-checking problems (with respect to an appropriate class of constraint automata) for this logic are decidable in polynomial space improving significantly known results about its strict fragments. As a by-product, LTL model-checking over integral relational automata is proved complete for polynomial space which contrasts with the known undecidability of its CTL counterpart. 1

over concrete domains