A criterion for separating process calculi

We introduce a new criterion, replacement freeness, to discern the relative expressiveness of process calculi. Intuitively, a calculus is strongly replacement free if replacing, within an enclosing context, a process that cannot perform any visible action by an arbitrary process never inhibits the capability of the resulting process to perform a visible action. We prove that there exists no compositional and interaction sensitive encoding of a not strongly replacement free calculus into any strongly replacement free one. We then define a weaker version of replacement freeness, by only considering replacement of closed processes, and prove that, if we additionally require the encoding to preserve name independence, it is not even possible to encode a non replacement free calculus into a weakly replacement free one. As a consequence of our encodability results, we get that many calculi equipped with priority are not replacement free and hence are not encodable into mainstream calculi like CCS and pi-calculus, that instead are strongly replacement free. We also prove that variants of pi-calculus with match among names, pattern matching or polyadic synchronization are only weakly replacement free, hence they are separated both from process calculi with priority and from mainstream calculi.Comment: In Proceedings EXPRESS'10, arXiv:1011.601

The quest for formalism in law. Ideals of systemicity and axiomatisability between utopianism and heuristic assertion

After the relationship between form and content in art and law is surveyed and the axiomatic approach to systemicity in both philosophy and law of both the classic and modern ages is scrutinised, the want of axiomatisability-in presence of correlations between axiomatism and law notwithstanding-is established. The very nucleus of any axiomatic system is that in some set of building blocks there are few foundation stones from which one given overall building can be built up in one given form and with the inherent necessity of that the operation, in the security of reaching the same end result, can be repeated by any actor at any future time. However, the relationship amongst the constituents of legal systems is not such as to allow to make up their edifice in exclusively one form, only if the procedure is defined and some constituents as foundation stones are designated. For legal systems are truly dynamic systems thoroughly built on substantive interconnections. Therefore they resist- albeit idealise-axiomatisation. In consequence, exclusively the heuristic value of the axiomatic ideal can be fully implemented and scholarly realised in the domain of law

Algebraic structuralism

This essay is about how the notion of “structure” in ontic structuralism might be made precise. More specifically, my aim is to make precise the idea that the structure of the world is (somehow) given by the relations inhering in the world, in such a way that the relations are ontologically prior to their relata. The central claim is the following: one can do so by giving due attention to the relationships that hold between those relations, by making use of certain notions from algebraic logic

Algebraic structuralism

This essay is about how the notion of “structure” in ontic structuralism might be made precise. More specifically, my aim is to make precise the idea that the structure of the world is (somehow) given by the relations inhering in the world, in such a way that the relations are ontologically prior to their relata. The central claim is the following: one can do so by giving due attention to the relationships that hold between those relations, by making use of certain notions from algebraic logic

Algebraic structuralism

This essay is about how the notion of “structure” in ontic structuralism might be made precise. More specifically, my aim is to make precise the idea that the structure of the world is (somehow) given by the relations inhering in the world, in such a way that the relations are ontologically prior to their relata. The central claim is the following: one can do so by giving due attention to the relationships that hold between those relations, by making use of certain notions from algebraic logic

The philosophy of European Law with "chaos out of order" set-up and functioning

In reconsideration of the composition and operation of European law, it is the description of its underlying mentality that may cast best light on the query whether European law is the extension of domestic laws or a sui generis product. As to its action, European law is destructive upon the survival of traditions of legal positivism, for it recalls post modern clichés rather. Like a solar system with planets, it is two-centred from the beginning, commissioning both implementation and judicial check to member states. As part of global post modernism, a) European law stems from artificial reality construction freed from particular historical experience and, indeed, anything given hic et nunc. By its operation, b) it dynamises large structures and sets in motion that what is chaos itself. It is owing to reconstructive human intent solely that any outcome can at all be seen as fitting to some ideal of order, albeit neither operation nor daily management strives for implementing any systemicity. This is the way in which the European law becomes adequate reflection of the underlying (macro) economic basis, which it is to serve as superstructure. Accordingly, c) the entire construct is operated (as integrated into one well-working unit) within the framework of an artificially animated dynamism. With its “order out of chaos” philosophy it assures member states’ standing involvement and competition, achieving a flexibly self-adapting (and unprecedentedly high degree of) conformity

On the Complexity of Deciding Behavioural Equivalences and Preorders. A Survey

This paper gives an overview of the computational complexity of all the equivalences in the linear/branching time hierarchy [vG90a] and the preordersin the corresponding hierarchy of preorders. We consider finite state or regular processes as well as infinite-state BPA [BK84b] processes. A distinction, which turns out to be important in the finite-state processes, is that of simulation-like equivalences/preorders vs. trace-like equivalencesand preorders. Here we survey various known complexity results for these relations. For regular processes, all simulation-like equivalences and preorders are decidable in polynomial time whereas all trace-like equivalences and preorders are PSPACE-Complete. We also consider interesting specialclasses of regular processes such as deterministic, determinate, unary, locally unary, and tree-like processes and survey the known complexity results inthese special cases. For infinite-state processes the results are quite different. For the class of context-free processes or BPA processes any preorder or equivalence beyond bisimulation is undecidable but bisimulation equivalence is polynomial timedecidable for normed BPA processes and is known to be elementarily decidable in the general case. For the class of BPP processes, all preorders and equivalences apart from bisimilarity are undecidable. However, bisimilarityis decidable in this case and is known to be decidable in polynomial time for normed BPP processes

Are Two Binary Operators Necessary to Finitely Axiomatise Parallel Composition?

Bergstra and Klop have shown that bisimilarity has a finite equational axiomatisation over ACP/CCS extended with the binary left and communication merge operators. Moller proved that auxiliary operators are necessary to obtain a finite axiomatisation of bisimilarity over CCS, and Aceto et al. showed that this remains true when Hennessy's merge is added to that language. These results raise the question of whether there is one auxiliary binary operator whose addition to CCS leads to a finite axiomatisation of bisimilarity. This study provides a negative answer to that question based on three reasonable assumptions

An algebra of behavioural types

Special thanks to Gérard Boudol, Ilaria Castellani, Silvano Dal Zilio, and Massimo Merro, for fruitful discussions and careful reading of parts of this document. Several anonymous referees made useful comments.We propose a process algebra, the Algebra of Behavioural Types, as a language for typing concurrent objects. A type is a higher-order labelled transition system that characterises all possible life cycles of a concurrent object. States represent interfaces of objects; state transitions model the dynamic change of object interfaces. Moreover, a type provides an internal view of the objects that inhabits it: a synchronous one, since transitions correspond to message reception. To capture this internal view of objects we define a notion of bisimulation, strong on labels and weak on silent actions. We study several algebraic laws that characterise this equivalence, and obtain completeness results for image-finite types.publishersversionpublishe