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Applicative Bisimulation and Quantum λ-Calculi
[chapter]
2015
Lecture Notes in Computer Science
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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]
2015
arXiv
pre-print
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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
2015
International Conference on Concurrency Theory
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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]
2012
arXiv
pre-print
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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]
2014
arXiv
pre-print
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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
2012
Electronic Proceedings in Theoretical Computer Science
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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]
2013
arXiv
pre-print
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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
2006
Mathematical Structures in Computer Science
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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]
2006
arXiv
pre-print
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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]
2021
arXiv
pre-print
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2020 pre-print arXiv:2007.08187v1 fatcat:rzlbnuf3izbnbmisoczy4cpdfuOther Versions
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
2021
Mathematics
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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]
2010
arXiv
pre-print
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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
2007
Electronical Notes in Theoretical Computer Science
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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
2020
Electronic Proceedings in Theoretical Computer Science
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2020 pre-print arXiv:2001.06942v1 fatcat:6c7lsfalb5fanluvezt7nvsqkq
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
2020
International Conference on Concurrency Theory
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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
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