Abstract: In the type frame originating from the flat domain of boolean values, we single out elements which are hereditarily total. We show that these elements can be defined, up to total equivalence, by sequential programs. The elements of an equivalence class of the totality equivalence relation (totality class) can be seen as different algorithms for computing a given set-theoretic boolean function. We show that the bottom element of a totality class, which is sequential, corresponds to the most eager algorithm, and the top to the laziest one. Finally we suggest a link between size of totality classes and a well known measure of complexity of boolean functions, namely their sensitivity.

Abstract: Basic properties of rewriting systems can be stated in the framework of abstract reduction systems (ARS). Properties like confluence (or Church-Rosser, CR) and weak confluence (or weak Church-Rosser, WCR) and their relationships can be studied in this setting: as a matter of fact, well-known counterexamples to the implication WCR CR have been formulated as ARS. In this paper, starting from the observation that such counterexamples are structurally similar, we set out a graph-theoretic characterization of WCR ARS that is not CR in terms of a suitable class of reduction graphs, such that in every WCR not CR ARS, we can embed at least one element of this class. Moreover, we give a tighter characterization for a restricted class of ARS enjoying a suitable regularity condition. Finally, as a consequence of our approach, we prove some interesting results about ARS using the mathematical tools developed. In particular, we prove an extension of the Newman’s lemma and we find out conditions that, once assumed together with WCR property, ensure the unique normal form property. The Appendix treats two interesting examples, both generated by graph-rewriting rules, with specific combinatorial properties.

Abstract: We consider a type discipline for the Ambient Calculus that associates ambients with security levels and constrains them to be traversed by or opened in ambients of higher security clearance only. We present a bottom-up algorithm that, given an untyped process P, computes a minimal set of constraints on security levels such that all actions during runs of P are performed without violating the security level priorities. Such an algorithm appears to be a prerequisite to use type systems to ensure security properties in the web scenario.

Abstract: We present an ambient-like calculus in which the open capability is dropped, and a new form of “lightweight� process mobility is introduced. The calculus comes equipped with a type system that allows the kind of values exchanged in communications and the access and mobility properties of processes to be controlled. A type inference procedure determines the “minimal� requirements to accept a system or a component as well typed. This gives a kind of principal typing. As an expressiveness test, we show that some well known calculi of concurrency and mobility can be encoded in our calculus in a natural way.

Abstract: We present two OBDD based model checking algorithms for the verification of Nash equilibria in finite state mechanisms modeling Multiple Administrative Domains (MAD) distributed systems with possibly colluding agents (coalitions) and with possibly faulty or malicious nodes (Byzantine agents). Given a finite state mechanism, a proposed protocol for each agent and the maximum sizes f for Byzantine agents and q for agents collusions, our model checkers return Pass if the proposed protocol is an ε-f-q-Nash equilibrium, i.e. no coalition of size up to q may have an interest greater than ε in deviating from the proposed protocol when up to f Byzantine agents are present, Fail otherwise. We implemented our model checking algorithms within the NuSMV model checker: the first one explicitly checks equilibria for each coalition, while the second represents symbolically all coalitions. We present experimental results showing their effectiveness for moderate size mechanisms. For example, we can verify coalition Nash equilibria for mechanisms which corresponding normal form games would have more than $5 \times 10^21$ entries. Moreover, we compare the two approaches, and the explicit algorithm turns out to outperform the symbolic one. To the best of our knowledge, no model checking algorithm for verification of Nash equilibria of mechanisms with coalitions has been previously published.