We investigate the satisfiability problem for a logic for true concurrency, whose formulae predicate about events in computations and their causal (in)dependencies. Variants of such logics have been studied, with different expressiveness, corresponding to a number of true concurrent behavioural equivalences. Here we focus on a mu-calculus style logic that represents the counterpart of history-preserving (hp-)bisimilarity, a typical equivalence in the true concurrent spectrum of bisimilarities. It is known that one can decide whether or not two 1-safe Petri nets (and in general finite asynchronous transition systems) are hp-bisimilar. Moreover, for the logic that captures hp-bisimilarity the model-checking problem is decidable with respect to prime event structures satisfying suitable regularity conditions. To the best of our knowledge, the problem of satisfiability has been scarcely investigated in the realm of true concurrent logics. We show that satisfiability for the logic for hp-bisimilarity is undecidable via a reduction from domino tilings. The fragment of the logic without fixpoints, instead, turns out to be decidable. We consider these results a first step towards a more complete investigation of the satisfiability problem for true concurrent logics, which we believe to have notable solvable cases.

The concept of non-interference has been introduced to characterise the absence of undesired information flows in a computing system. Although it is often explained referring to an informal notion of causality - the activity involving the part of the system with higher level of confidentiality should not cause any observable effect at lower levels - it is almost invariably formalised in terms of interleaving semantics. Here we focus on Petri nets and on the BNDC (Bisimilarity-based Non-Deducibility on Composition) property, a formalisation of non-interference widely studied in the literature. We show that BNDC admits natural characterisations based on the unfolding semantics - a classical true concurrent semantics for Petri nets - in terms of causalities and conflicts between high and low level activities. This leads to algorithms for checking BNDC on various classes of Petri nets, based on the construction of suitable complete prefixes of the unfolding. We also developed a prototype tool UBIC (Unfolding-Based Interference Checker), working on safe Petri nets, which provides promising results in terms of efficiency.

A longstanding open problem is whether there exists a model of the untyped lambda calculus in the category CPO of complete partial orderings and Scott continuous functions, whose theory is exactly the least lambda-theory lambda-beta or the least extensional lambda-theory lambda-beta-eta. In this paper we analyze the class of reflexive Scott domains, the models of lambda-calculus living in the category of Scott domains (a full subcategory of CPO). The following are the main results of the paper: (i) Extensional reflexive Scott domains are not complete for the beta-eta-calculus, i.e., there are equations not in lambda-beta-eta which hold in all extensional reflexive Scott domains.(ii) The order theory of an extensional reflexive Scott domain is never recursively enumerable. These results have been obtained by isolating among the reflexive Scott domains a class of webbed models arising from Scott's information systems, called iweb-models. The class of iweb-models includes all extensional reflexive Scott domains, all preordered coherent models and all filter models living in CPO. Based on a fine-grained study of an ``effective'' version of Scott's information systems, we have shown that there are equations not in lambda-beta (resp. lambda-beta-eta) which hold in all (extensional) iweb-models.