Filters








56 Hits in 2.9 sec

Applicative Bisimulation and Quantum λ-Calculi [chapter]

Ugo Dal Lago, Alessandro Rioli
2015 Lecture Notes in Computer Science  
In this paper we show that applicative bisimulation also works when the underlying language of programs takes the form of a linear λcalculus extended with features such as probabilistic binary choice,  ...  Applicative bisimulation is a coinductive technique to check program equivalence in higher-order functional languages.  ...  Conclusions We show that Abramsky's applicative bisimulation can be adapted to linear λcalculi endowed with probabilistic choice and quantum data.  ... 
doi:10.1007/978-3-319-24644-4_4 fatcat:cgxlelylhzc3do6m4af5cbyhai

Applicative Bisimulation and Quantum λ-Calculi (Long Version) [article]

Ugo Dal Lago, Alessandro Rioli
2015 arXiv   pre-print
In this paper we show that applicative bisimulation also works when the underlying language of programs takes the form of a linear λ-calculus extended with features such as probabilistic binary choice,  ...  Applicative bisimulation is a coinductive technique to check program equivalence in higher-order functional languages.  ...  Conclusions We show that Abramsky's applicative bisimulation can be adapted to linear λ-calculi endowed with probabilistic choice and quantum data.  ... 
arXiv:1506.06661v1 fatcat:kgmpija4ozgsfh63entfvnqshy

On Coinduction and Quantum Lambda Calculi

Yuxin Deng, Yuan Feng, Ugo Dal Lago, Marc Herbstritt
2015 International Conference on Concurrency Theory  
We introduce a linear contextual equivalence and two notions of bisimilarity, a state-based and a distribution-based, as proof techniques for reasoning about higher-order quantum programs.  ...  In the ubiquitous presence of linear resources in quantum computation, program equivalence in linear contexts, where programs are used or executed once, is more important than in the classical setting.  ...  Recently, the third author and Rioli have studied applicative bisimulation in a purely linear quantum λ-calculus, obtaining a soundness result [3] .  ... 
doi:10.4230/lipics.concur.2015.427 dblp:conf/concur/DengFL15 fatcat:ovlucp26zfcdde5o5vdmwybnne

Open Bisimulation for Quantum Processes [article]

Yuxin Deng, Yuan Feng
2012 arXiv   pre-print
We propose a notion of open bisimulation for quantum processes and show that it provides both a sound and complete proof methodology for a natural extensional behavioural equivalence between quantum processes  ...  We also give a modal characterisation of open bisimulation, by extending the Hennessy-Milner logic to a quantum setting.  ...  It is easy to prove that the bisimulation in [10] is both a ground bisimulation and closed under superoperator application.  ... 
arXiv:1201.0416v1 fatcat:ubsxtrxccnfhbdic7zgiv4eity

What are the fundamental structures of concurrency? We still don't know! [article]

Samson Abramsky
2014 arXiv   pre-print
Some fleeting glimpses are sought from Petri Nets, physics and geometry.  ...  A major recent development in process calculi has been their application to biological modelling.  ...  and topological quantum field theories.5  ... 
arXiv:1401.4973v1 fatcat:xpfawrxcfnfbxomlhrd3vgh5ii

Analysis of a Quantum Error Correcting Code using Quantum Process Calculus

Timothy A. S. Davidson, Simon J. Gay, Rajagopal Nagarajan, Ittoop Vergheese Puthoor
2012 Electronic Proceedings in Theoretical Computer Science  
We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science.  ...  The key idea is to define two systems, one modelling a protocol and one expressing a specification, and prove that they are behaviourally equivalent.  ...  Quantum process calculi have been developed as part of a programme to transfer ideas from the field of formal methods, well established within classical computer science, to quantum systems.  ... 
doi:10.4204/eptcs.95.7 fatcat:mia3zb75yjhf7oy5vnyl2vr6ey

Probabilistic bisimilarities between quantum processes [article]

Yuan Feng, Runyao Duan, Zhengfeng Ji, Mingsheng Ying
2013 arXiv   pre-print
Modeling and reasoning about concurrent quantum systems is very important both for distributed quantum computing and for quantum protocol verification.  ...  For this purpose, we propose a model qCCS which is a natural quantum extension of classical value-passing CCS with the input and output of quantum states, and unitary transformations and measurements on  ...  Acknowledgement The authors thank the colleagues in the Quantum Computation and Quantum Information Research Group for useful discussion. This work was partly supported by the Natural Science  ... 
arXiv:cs/0601014v3 fatcat:fqyf3avskvbevajdz6jtjpsazy

Relations among quantum processes: bisimilarity and congruence

MARIE LALIRE
2006 Mathematical Structures in Computer Science  
Moreover, to model concurrent and distributed quantum computations and quantum communication protocols, communications over quantum channels which move qubits physically from one place to another must  ...  This notation provides a homogeneous style to formal descriptions of concurrent and distributed computations comprising both quantum and classical parts.  ...  Several quantum λ-calculi have also been developed: for example (van Tonder 2003) by Van Tonder, based on a simplified linear λ-calculus and (Arrighi and Dowek 2004) by Arrighi and Dowek, which is  ... 
doi:10.1017/s096012950600524x fatcat:bxzwn3nsezat7i57aaajrmnhry

Relations among quantum processes: bisimilarity and congruence [article]

Marie Lalire
2006 arXiv   pre-print
Moreover, to model concurrent and distributed quantum computations and quantum communication protocols, communications over quantum channels which move qubits physically from one place to another must  ...  This notation provides a homogeneous style to formal descriptions of concurrent and distributed computations comprising both quantum and classical parts.  ...  Several quantum λ-calculi have also been developed: for example (van Tonder 2003) by Van Tonder, based on a simplified linear λ-calculus and (Arrighi and Dowek 2004) by Arrighi and Dowek, which is  ... 
arXiv:quant-ph/0603274v1 fatcat:4ilavafsibd2fknvx4mvt5s7ly

Processes, Systems & Tests: Defining Contextual Equivalences [article]

Clément Aubert, Daniele Varacca
2021 arXiv   pre-print
comparisons takes place – that play multiple distinct roles but supposedly always stay the same.We illustrate our statement with a simple Java example, the usual concurrent languages, but also back it up with λ-calculus  ...  our layered model of development will clarify the distinction that is too often left implicit between the tasks and duties of the programmer and of the tester.  ...  Processes, Systems and Tests As in the λ-calculus, most concurrent calculi make a distinction between open and closed terms.  ... 
arXiv:2007.08187v3 fatcat:gqyzeua2t5aj7f5kbaj6ma3eo4

Fuzzy Automata as Coalgebras

Ai Liu, Shun Wang, Luis Soares Barbosa, Meng Sun
2021 Mathematics  
Based on the coalgebraic models, we can define a notion of fuzzy language and consider several versions of bisimulation for fuzzy automata.  ...  A group of combinators is defined to compose fuzzy automata of two branches: state transition and output function. A case study illustrates the coalgebraic models proposed and their composition.  ...  Many thanks to the reviewers and editors. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math9030272 fatcat:vj3s44nm45ckbcbi5jksgbpjay

Knots as processes: a new kind of invariant [article]

L.G. Meredith, David F. Snyder
2010 arXiv   pre-print
We exhibit an encoding of knots into processes in the π-calculus such that knots are ambient isotopic if and only their encodings are weakly bisimilar.  ...  The authors wish to thank Matthias Radestock for suggestions for coding wires, and early advocation of the wire-saturated form the final encoding took and his probing questions regarding proof strategies  ...  This line of thought seems particularly strengthened when we recall the πcalculus is just one of many 'computational calculi' -the λ-calculus being another paradigmatic example-that may be thought of as  ... 
arXiv:1009.2107v1 fatcat:f6hgdrx7svactg27hpwv6bipeq

Modelling the Security of Smart Cards by Hard and Soft Types for Higher-Order Mobile Embedded Resources

Mikkel Bundgaard, Thomas Hildebrandt, Jens Chr. Godskesen
2007 Electronical Notes in Theoretical Computer Science  
non-linear (copyable) higher-order mobile processes, nested locations, and local names.  ...  type system inspired by affine intuitionistic logic for the calculus of Higher-Order Mobile Embedded Resources (Homer), resulting in the first process calculus combining affine linear (non-copyable) and  ...  We expect to investigate other variations and applications of linear types and more expressive type systems for Homer within the research projects for Mobile Security and Computer Supported Mobile Adaptive  ... 
doi:10.1016/j.entcs.2007.09.011 fatcat:2lfoacyso5bblp74q47rfqswne

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

Alessandro Aldini
2020 Electronic Proceedings in Theoretical Computer Science  
Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security.  ...  The aim of this survey is to revisit such achievements and results from the standpoint of QAPL and its community.  ...  , with applications to the economic domain.  ... 
doi:10.4204/eptcs.312.1 fatcat:4fjvygbppjbq3k5ury2kvue3nq

How Reversibility Can Solve Traditional Questions: The Example of Hereditary History-Preserving Bisimulation

Clément Aubert, Ioana Cristescu, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
This bisimulation captures classical equivalences relations for denotational models of concurrency (history- and hereditary history-preserving bisimulation, (H)HPB), that were up to now only partially  ...  Concurrent reversible computation, for instance, offered interesting extensions to the Calculus of Communicating Systems, but was still lacking a natural and pertinent bisimulation to study processes equivalences  ...  (m λ.P + Q) −−− → i:λ i, λ, Q .m P R −−− → i:λ R S −−− → i:λ S syn.  ... 
doi:10.4230/lipics.concur.2020.7 dblp:conf/concur/AubertC20 fatcat:7x2yr2gp2zdshcv7si7k4byqxu
« Previous Showing results 1 — 15 out of 56 results