570 research outputs found
Unifying type systems for mobile processes
We present a unifying framework for type systems for process calculi. The
core of the system provides an accurate correspondence between essentially
functional processes and linear logic proofs; fragments of this system
correspond to previously known connections between proofs and processes. We
show how the addition of extra logical axioms can widen the class of typeable
processes in exchange for the loss of some computational properties like
lock-freeness or termination, allowing us to see various well studied systems
(like i/o types, linearity, control) as instances of a general pattern. This
suggests unified methods for extending existing type systems with new features
while staying in a well structured environment and constitutes a step towards
the study of denotational semantics of processes using proof-theoretical
methods
Process Algebras
Process Algebras are mathematically rigorous languages with well defined semantics that permit describing and verifying properties of concurrent communicating systems.
They can be seen as models of processes, regarded as agents that act and interact continuously with other similar agents and with their common environment. The agents may be real-world objects (even people), or they may be artifacts, embodied perhaps in computer hardware or software systems.
Many different approaches (operational, denotational, algebraic) are taken for describing the meaning of processes. However, the operational approach is the reference one. By relying on the so called Structural Operational Semantics (SOS), labelled transition systems are built and composed by using the different operators of the many different process algebras. Behavioral equivalences are used to abstract from unwanted details and identify those systems that react similarly to external
experiments
A formal model of asynchronous communication and its use in mechanically verifying a biphase mark protocol
In this paper we present a formal model of asynchronous communication as a function in the Boyer-Moore logic. The function transforms the signal stream generated by one processor into the signal stream consumed by an independently clocked processor. This transformation 'blurs' edges and 'dilates' time due to differences in the phases and rates of the two clocks and the communications delay. The model can be used quantitatively to derive concrete performance bounds on asynchronous communications at ISO protocol level 1 (physical level). We develop part of the reusable formal theory that permits the convenient application of the model. We use the theory to show that a biphase mark protocol can be used to send messages of arbitrary length between two asynchronous processors. We study two versions of the protocol, a conventional one which uses cells of size 32 cycles and an unconventional one which uses cells of size 18. We conjecture that the protocol can be proved to work under our model for smaller cell sizes and more divergent clock rates but the proofs would be harder
Functionality, Polymorphism, and Concurrency: A Mathematical Investigation of Programming Paradigms
The search for mathematical models of computational phenomena often leads to problems that are of independent mathematical interest. Selected problems of this kind are investigated in this thesis. First, we study models of the untyped lambda calculus. Although many familiar models are constructed by order-theoretic methods, it is also known that there are some models of the lambda calculus that cannot be non-trivially ordered. We show that the standard open and closed term algebras are unorderable. We characterize the absolutely unorderable T-algebras in any algebraic variety T. Here an algebra is called absolutely unorderable if it cannot be embedded in an orderable algebra. We then introduce a notion of finite models for the lambda calculus, contrasting the known fact that models of the lambda calculus, in the traditional sense, are always non-recursive. Our finite models are based on Plotkin’s syntactical models of reduction. We give a method for constructing such models, and some examples that show how finite models can yield useful information about terms. Next, we study models of typed lambda calculi. Models of the polymorphic lambda calculus can be divided into environment-style models, such as Bruce and Meyer’s non-strict set-theoretic models, and categorical models, such as Seely’s interpretation in PL-categories. Reynolds has shown that there are no set-theoretic strict models. Following a different approach, we investigate a notion of non-strict categorical models. These provide a uniform framework in which one can describe various classes of non-strict models, including set-theoretic models with or without empty types, and Kripke-style models. We show that completeness theorems correspond to categorical representation theorems, and we reprove a completeness result by Meyer et al. on set-theoretic models of the simply-typed lambda calculus with possibly empty types. Finally, we study properties of asynchronous communication in networks of communicating processes. We formalize several notions of asynchrony independently of any particular concurrent process paradigm. A process is asynchronous if its input and/or output is filtered through a communication medium, such as a buffer or a queue, possibly with feedback. We prove that the behavior of asynchronous processes can be equivalently characterized by first-order axioms
Integrated Modeling and Verification of Real-Time Systems through Multiple Paradigms
Complex systems typically have many different parts and facets, with
different characteristics. In a multi-paradigm approach to modeling, formalisms
with different natures are used in combination to describe complementary parts
and aspects of the system. This can have a beneficial impact on the modeling
activity, as different paradigms an be better suited to describe different
aspects of the system. While each paradigm provides a different view on the
many facets of the system, it is of paramount importance that a coherent
comprehensive model emerges from the combination of the various partial
descriptions. In this paper we present a technique to model different aspects
of the same system with different formalisms, while keeping the various models
tightly integrated with one another. In addition, our approach leverages the
flexibility provided by a bounded satisfiability checker to encode the
verification problem of the integrated model in the propositional
satisfiability (SAT) problem; this allows users to carry out formal
verification activities both on the whole model and on parts thereof. The
effectiveness of the approach is illustrated through the example of a
monitoring system.Comment: 27 page
Multiparty Sessions based on Proof Nets
We interpret Linear Logic Proof Nets in a term language based on Solos
calculus. The system includes a synchronisation mechanism, obtained by a
conservative extension of the logic, that enables to define non-deterministic
behaviours and multiparty sessions.Comment: In Proceedings PLACES 2014, arXiv:1406.331
Bisimulations for Asynchronous Mobile Processes
Within the past few years there has been renewed interest in thestudy of value-passing process calculi as a consequence of the emergence of the pi-calculus. Here, [MPW89] have determined two variants of the notion of bisimulation, late and early bisimilarity. Most recently [San93] has proposed the new notion of open bisimulation equivalence. In this paper we consider Plain LAL, a mobile process calculus which differs from the pi-calculus in the sense that the communication of data values happens asynchronously. The surprising result is that in the presence of asynchrony, the open, late and early bisimulation equivalences coincide - this in contrast to the pi-calculus where they are distinct. The result allows us to formulate a common equational theory which is sound and complete for finite terms of Plain LAL
A non-interleaving process calculus for multi-party synchronisation
We introduce the wire calculus. Its dynamic features are inspired by Milner's
CCS: a unary prefix operation, binary choice and a standard recursion
construct. Instead of an interleaving parallel composition operator there are
operators for synchronisation along a common boundary and non-communicating
parallel composition. The (operational) semantics is a labelled transition
system obtained with SOS rules. Bisimilarity is a congruence with respect to
the operators of the language. Quotienting terms by bisimilarity results in a
compact closed category
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