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Interpreting a finitary pi-calculus in differential interaction nets

Thomas Ehrhard, Olivier Laurent
2010 Information and Computation  
We propose and study a translation of a pi-calculus without sums nor recursion into an untyped version of differential interaction nets.  ...  one, but two free ports in the corresponding differential interaction net.  ...  This does not mean of course that differential interaction nets cannot interpret these features. We shortly discuss this point in the Conclusion.  ... 
doi:10.1016/j.ic.2009.06.005 fatcat:4fwmomneuzgwjdihbbqvqenzmi

Interpreting a Finitary Pi-calculus in Differential Interaction Nets [chapter]

Thomas Ehrhard, Olivier Laurent
Lecture Notes in Computer Science  
We propose and study a translation of a pi-calculus without sums nor recursion into an untyped version of differential interaction nets.  ...  one, but two free ports in the corresponding differential interaction net.  ...  This does not mean of course that differential interaction nets cannot interpret these features. We shortly discuss this point in the Conclusion.  ... 
doi:10.1007/978-3-540-74407-8_23 fatcat:fpb4eh57tbekndoxxqgdr6k2si

Acyclic Solos and Differential Interaction Nets

Thomas Ehrhard, Olivier Laurent, Davide Sangiorgi
2010 Logical Methods in Computer Science  
This gives a (new) proof that differential interaction nets are expressive enough to contain an encoding of the pi-calculus.  ...  In particular, the induced solo diagrams bear an acyclicity property that induces a faithful encoding into differential interaction nets.  ...  We developed in a previous paper [EL10] a translation between the π-calculus [MPW92] and differential interaction nets [ER06] .  ... 
doi:10.2168/lmcs-6(3:11)2010 fatcat:tppnydr5rndpfhpdep3fdplzq4

Finitary Spacetime Sheaves of Quantum Causal Sets: Curving Quantum Causality [article]

A. Mallios, I. Raptis
2001 arXiv   pre-print
A_n is physically interpreted as the dynamical field of a locally finite quantum causality, while its associated curvature F_n, as some sort of 'finitary Lorentzian quantum gravity.  ...  A locally finite, causal and quantal substitute for a locally Minkowskian principal fiber bundle P of modules of Cartan differential forms over a bounded region X of a curved C^∞-smooth differential manifold  ...  calculus on a discrete differential manifold is flat, in that it reduces to the nilpotent Kähler-Cartan differential D whose curvature R is zero, since R := ∇ 2 = D 2 = 0. 19 In GR, the local metric field  ... 
arXiv:gr-qc/0102097v1 fatcat:ja4anqjwkrhcjocrzqolkfuofu

Presheaves, Sheaves and their Topoi in Quantum Gravity and Quantum Logic [article]

Ioannis Raptis
2001 arXiv   pre-print
A brief synopsis of recent conceptions and results, the current status and future outlook of our research program of applying sheaf and topos-theoretic ideas to quantum gravity and quantum logic is presented  ...  The present work was supported by the European Union in the form of a generous Marie Curie Individual Postdoctoral Research Fellowship held at Imperial College, London (United Kingdom).  ...  Geometry theory [43, 44, 45, 46] , with Chris Mulvey (University of Sussex) on quantales and noncommutative topology, as well as a brief but timely exchange with Bob Coecke (Oxford) on a promising dynamical  ... 
arXiv:gr-qc/0110064v1 fatcat:kni7qpgc65cgte4qsiczclpvgq

Finitary, Causal and Quantal Vacuum Einstein Gravity [article]

Anastasios Mallios, Ioannis Raptis
2002 arXiv   pre-print
We continue recent work and formulate the gravitational vacuum Einstein equations over a locally finite spacetime by using the basic axiomatics, techniques, ideas and working philosophy of Abstract Differential  ...  The whole construction is 'fully covariant', 'inherently quantum' (both expressions are analytically explained in the paper) and genuinely smooth background spacetime independent.  ...  for funding this work via a Marie Curie postdoctoral research fellowship held at Imperial College.  ... 
arXiv:gr-qc/0209048v6 fatcat:bbs2zdly3nddjegc46nxxqxzia

Radiative Transfer on Discrete Spaces

Rudolph W. Preisendorfer, T. Teichmann
1966 Physics today  
Each point of the set is then assigned certain scattering and absorbing properties with respect to impinging radiant energy, and each is generally allowed to interact radiometrically in a specified way  ...  bounded set of points, finite in number, each of which is located in E3 in accordance with some explicit rule of selection.  ...  However, this criticism can be directed only at the calculus level. It will be admitted that the calculus of finitary formulations is presently not as well developed as the infinitary formulations.  ... 
doi:10.1063/1.3047924 fatcat:ab2oetqfrfcgropnxjwm4z7pqi

Game Semantics: Easy as Pi [article]

Nobuko Yoshida, Simon Castellan, Léo Stefanesco
2020 arXiv   pre-print
In this paper, we aim at making game semantics more accessible by viewing it as a syntactic translation into a session typed pi-calculus, referred to as metalanguage, followed by a semantics interpretation  ...  We give a causal and non-angelic game semantics model using event structures, which supports a simple semantics interpretation of PiDiLL.  ...  In the context of proof-nets, Ehrhard and Laurent [2010] investigate encoding a finitary -calculus in a transition system of labelled differential interaction nets.  ... 
arXiv:2011.05248v1 fatcat:ambmnowganhfjd2azbf55x4w34

Proofs as Executions [chapter]

Emmanuel Beffara, Virgile Mogbil
2012 Lecture Notes in Computer Science  
This paper proposes a new interpretation of the logical contents of programs in the context of concurrent interaction, wherein proofs correspond to valid executions of a processes.  ...  to executing the process in a given interaction scenario.  ...  In a different style, differential logic was recently developed by Ehrhard and Regnier [8] and its untyped proof formalism was shown expressive enough to represent the π-calculus [7] .  ... 
doi:10.1007/978-3-642-33475-7_20 fatcat:oqbzzkfswfawxagsxkvkqscage

On fixpoint logics and equivalences for processes with restricted nondeterminism

Julian Gutierrez
2015 Journal of Logic and Computation  
, the so-called 'true concurrency' approach, independence or concurrency is a primitive notion (as in, e.g., Petri nets or event structures) rather than a derived concept, as in the interleaving framework  ...  In concurrency, processes can be studied using a partial order or an interleaving semantics.  ...  The first part of this paper is an extended and revised version of [11] ; the second and third parts are based on unpublished results initially studied in [12] .  ... 
doi:10.1093/logcom/exv032 fatcat:lnpbai3nvzcgxgbvauammc2yge

Algebraic specification of concurrent systems

Stéphane Kaplan
1989 Theoretical Computer Science  
A primitive for putting specifications together, in parellel, is analyzed. Finally, richer primitives for building basic specifications are discussed.  ...  Processes apply to data via an application operator, eventually yielding a set of data as a result.  ...  behave as an atomic action (axiom (m) is interpreted likewise).  ... 
doi:10.1016/0304-3975(89)90090-x fatcat:csvdqifnsjaslgh4jiujlwx42q

Twenty Years of Rewriting Logic [chapter]

José Meseguer
2010 Lecture Notes in Computer Science  
This paper provides a gentle, intuitive introduction to its main ideas, as well as a survey of the work that many researchers have carried out over the last twenty years in advancing: (i) its foundations  ...  Rewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality.  ...  This work has been supported in part by NSF Grants CNS 07-16638, CNS 08-34709, CNS 08-31064, CNS 09-04749, and CCF 09-05584, AFOSR Grant FA8750-11-2-0084, and the "Programa de Apoyo a la Investigación  ... 
doi:10.1007/978-3-642-16310-4_2 fatcat:ho7s76r67nc63bndpoptbh5k4e

Twenty years of rewriting logic

José Meseguer
2012 The Journal of Logic and Algebraic Programming  
This paper provides a gentle, intuitive introduction to its main ideas, as well as a survey of the work that many researchers have carried out over the last twenty years in advancing: (i) its foundations  ...  Rewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality.  ...  This work has been supported in part by NSF Grants CNS 07-16638, CNS 08-34709, CNS 08-31064, CNS 09-04749, and CCF 09-05584, AFOSR Grant FA8750-11-2-0084, and the "Programa de Apoyo a la Investigación  ... 
doi:10.1016/j.jlap.2012.06.003 fatcat:5tx4a5uxlvapfpf5fajozkbboi

Logical concepts in cryptography

Simon Kramer
2007 ACM SIGACT News  
Subject This thesis is about a breadth-first exploration of logical concepts in cryptography and their linguistic abstraction and model-theoretic combination in a comprehensive logical system, called CPL  ...  Synopsis This thesis is about a breadth-first exploration of logical concepts in cryptography and their linguistic abstraction and model-theoretic combination in a comprehensive logical system, called  ...  constructive criticism of my work; Marc De Falco for his exploratory (now superseded) contribution to my work at an experimental stage; Christoph Frei for his elder-brotherly advice on the practice of being a  ... 
doi:10.1145/1345189.1345205 fatcat:wyk6rfbagbfwrasry7ohjjbq5q

The summer meeting in Seattle

V. L. Klee Jr.
1956 Bulletin of the American Mathematical Society  
Gâl: On the fundamental theorems of the differential and integral calculus.  ...  Given n points Pi, P2, • • • , P w in an arbitrary space, and the distance d (Pi, Pj) =au>0 for every pair of distinct points P t -and Pj, we define the weight W% of the point Pi by Wi-]C/ a u an d the  ...  Consider the differential equation (1) x(0) =c where $(x) is a continuous function of x satisfying additional conditions ensuring the existence of a unique solution over the interval O^t^T for a ^c  ... 
doi:10.1090/s0002-9904-1956-10067-0 fatcat:psguzmtiurgxxaranalbw7fh2y
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