scholarly journals Computability structures, simulations and realizability

2013 ◽  
Vol 24 (2) ◽  
Author(s):  
JOHN LONGLEY
Keyword(s):  
Wide Class ◽  
General Notion ◽  
Process Algebras ◽  
Computational Power ◽  
Closure Properties ◽  
Transition Systems ◽  
Labelled Transition Systems ◽  
Wide Range ◽  
Standard Construction ◽  
Cartesian Closed

We generalise the standard construction of realizability models (specifically, of categories of assemblies) to a wide class ofcomputability structures, which is broad enough to embrace models of computation such as labelled transition systems and process algebras. We consider a general notion ofsimulationbetween such computability structures, and show how these simulations correspond precisely to certain functors between the realizability models. Furthermore, we show that our class of computability structures has good closure properties – in particular, it is ‘cartesian closed’ in a slightly relaxed sense. Finally, we investigate some important subclasses of computability structures and of simulations between them. We suggest that our 2-category of computability structures and simulations may offer a useful framework for investigating questions of computational power, abstraction and simulability for a wide range of models.

scholarly journals On the Finitary Bisimulation

1995 ◽  
Vol 2 (59) ◽  
Author(s):  
Luca Aceto ◽  
Anna Ingólfsdóttir
Keyword(s):  
Denotational Semantics ◽  
Subject Classification ◽  
Process Algebras ◽  
Transition Systems ◽  
Behavioural Observation ◽  
Labelled Transition Systems ◽  
Full Abstraction ◽  
Ams Subject Classification ◽  
Keywords And Phrases

<p>The finitely observable, or finitary, part of bisimulation is a key tool in establishing full abstraction results for denotational semantics for process algebras with respect to bisimulation-based preorders. A bisimulation-like characterization of this relation for arbitrary transition systems is given, relying on Abramsky's characterization in terms of the finitary domain logic. More informative behavioural, observation-independent characterizations of the finitary bisimulation are also offered for several interesting classes of transition systems. These include transition systems with countable action sets, those that have bounded convergent sort and the sort-finite ones. The result for sort-finite transition systems sharpens a previous behavioural characterization of the finitary bisimulation for this class of structures given by Abramsky.</p><p><br />AMS Subject Classification (1991): 68Q10 (Modes of computation), 68Q55<br />(Semantics), 03B70 (Logic of Programming), 68Q90 (Transition nets).<br />Keywords and Phrases: Concurrency, labelled transition systems with divergence,<br />bisimulation preorder, finitary relations, domain logic for transition systems.</p>

scholarly journals A uniform approach to domain theory in realizability models

1997 ◽  
Vol 7 (5) ◽  
pp. 469-505 ◽  
Author(s):  
JOHN R. LONGLEY ◽  
ALEX K. SIMPSON
Keyword(s):  
Wide Class ◽  
Lambda Calculus ◽  
Domain Theory ◽  
Closure Properties ◽  
Strong Completeness ◽  
Sequential Computation ◽  
Uniform Approach ◽  
Wide Range ◽  
Completeness Axiom

We propose a uniform way of isolating a subcategory of predomains within the category of modest sets determined by a partial combinatory algebra (PCA). Given a divergence on a PCA (which determines a notion of partiality), we identify a candidate category of predomains, the well-complete objects. We show that, whenever a single strong completeness axiom holds, the category satisfies appropriate closure properties. We consider a range of examples of PCAs with associated divergences and show that in each case the axiom does hold. These examples encompass models allowing a ‘parallel’ style of computation (for example, by interleaving), as well as models that seemingly allow only ‘sequential’ computation, such as those based on term-models for the lambda-calculus. Thus, our approach provides a uniform approach to domain theory across a wide class of realizability models. We compare our treatment with previous approaches to domain theory in realizability models. It appears that no other approach applies across such a wide range of models.

scholarly journals Dynamic game semantics

2020 ◽  
pp. 1-60
Author(s):  
Norihiro Yamada ◽  
Samson Abramsky
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Operational Semantics ◽  
Dynamic Game ◽  
Standard Interpretation ◽  
Functional Programming Languages ◽  
Game Semantics ◽  
Wide Range ◽  
Cartesian Closed Categories ◽  
Cartesian Closed

Abstract The present work achieves a mathematical, in particular syntax-independent, formulation of dynamics and intensionality of computation in terms of games and strategies. Specifically, we give game semantics of a higher-order programming language that distinguishes programmes with the same value yet different algorithms (or intensionality) and the hiding operation on strategies that precisely corresponds to the (small-step) operational semantics (or dynamics) of the language. Categorically, our games and strategies give rise to a cartesian closed bicategory, and our game semantics forms an instance of a bicategorical generalisation of the standard interpretation of functional programming languages in cartesian closed categories. This work is intended to be a step towards a mathematical foundation of intensional and dynamic aspects of logic and computation; it should be applicable to a wide range of logics and computations.

scholarly journals The first boundary value problem of the dynamics of an anisotropic elastic half-space under the action of subsonic transport loads

2020 ◽  
Vol 4 (78) ◽  
pp. 45-52
Author(s):  
G. K. ZAKIR’YANOVA ◽  
◽  
L. A. ALEXEYEVA ◽  
Keyword(s):  
Rock Mass ◽  
Boundary Value Problem ◽  
Half Space ◽  
Wide Class ◽  
Boundary Value ◽  
Operator Method ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Wide Range ◽  
Anisotropic Elastic

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.

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