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Symmetry Reduction for the Local Mu-Calculus [article]

Kedar S. Namjoshi, Richard J. Trefler
2019 arXiv   pre-print
Considerably generalizing earlier results on invariance, it is shown that all local mu-calculus properties, including safety and liveness properties, are preserved by neighborhood symmetries.  ...  For many network topologies, even those with little global symmetry, analysis with representatives provides a significant, even exponential, reduction in the cost of verification.  ...  Allen Emerson for inspiring discussions on the topic.  ... 
arXiv:1903.10405v1 fatcat:wrwngfzwvrem3lcuiiiqgsttty

Symmetry Reduction for the Local Mu-Calculus [chapter]

Kedar S. Namjoshi, Richard J. Trefler
2018 Lecture Notes in Computer Science  
Considerably generalizing earlier results on invariance, it is shown that all local mu-calculus properties, including safety and liveness properties, are preserved by neighborhood symmetries.  ...  For many network topologies, even those with little global symmetry, analysis with representatives provides a significant, even exponential, reduction in the cost of verification.  ...  Allen Emerson for inspiring discussions on the topic.  ... 
doi:10.1007/978-3-319-89963-3_22 fatcat:xhuau3tcpjayxnvq273r7jngxi

Strong Normalization of $\overline{\lambda}\mu\widetilde{\mu}$ -Calculus with Explicit Substitutions [chapter]

Emmanuel Polonovski
2004 Lecture Notes in Computer Science  
The λµμ-calculus, defined by Curien and Herbelin [7] , is a variant of the λµ-calculus that exhibits symmetries such as term/context and call-by-name/call-by-value.  ...  For that purpose, we first prove SN of simply typed λµμcalculus (by a variant of the reducibility technique from Barbanera and Berardi [2]), then we formalize a proof technique of SN via PSN (preservation  ...  namely those concerning reductions of the original calculus: β, β, mu, mu, sv and se.  ... 
doi:10.1007/978-3-540-24727-2_30 fatcat:7zbsfvgh4ne3fbklq3er2cyiwi

Call-by-name reduction and cut-elimination in classical logic

Kentaro Kikuchi
2008 Annals of Pure and Applied Logic  
The isomorphism preserves β, µ-reduction, which is simulated by a local-step cut-elimination procedure in the typed case, where the reduction system strictly follows the "cut=redex" paradigm.  ...  strongly normalizing local-step cut-elimination procedure for classical logic  ...  I was much inspired by Daisuke Kimura and Stéphane Lengrand on the subject of this paper. I also thank Izumi Takeuti and the anonymous referees for valuable comments.  ... 
doi:10.1016/j.apal.2008.01.002 fatcat:uni7f3ftt5g5zbhju7ug53q6ca

Lie Symmetry Analysis and Explicit Solutions of the Time Fractional Fifth-Order KdV Equation

Gang wei Wang, Tian zhou Xu, Tao Feng, Duccio Rocchini
2014 PLoS ONE  
In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained.  ...  A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed.  ...  Next, we can find that the parameters affect the symmetry and other properties of the equation, such as the symmetry reductions and so on.  ... 
doi:10.1371/journal.pone.0088336 pmid:24523885 pmcid:PMC3921151 fatcat:plawiz6zlrao3cfx3xy2yvwfyy

Symmetry and model checking [chapter]

E. Allen Emerson, A. Prasad Sistla
1993 Lecture Notes in Computer Science  
If we further stipulate that G be contained in Aut .M N Aul f then we get a precise correspondence enabling us to establish 2td,s~]' iff Ad,~f where f is a formula of CTL* or Mu-Calculus, and g indicates  ...  We show how to exploit symmetry in model checking for concurrent systems containing many identical or isomorphic components. We focus in particular on those composed of many isomorphic processes.  ...  Acknowledgements and Historical Remark We have been thinking about this problem for some time. Actually, we had the Correspondence Lemma 3.1 in 1988 but encountered other difficulties.  ... 
doi:10.1007/3-540-56922-7_38 fatcat:5wfran33rzg3ditekfvrmdmh6i

Functions as Processes: Termination and the $\lambda\mu\widetilde{\mu}$ -Calculus [chapter]

Matteo Cimini, Claudio Sacerdoti Coen, Davide Sangiorgi
2010 Lecture Notes in Computer Science  
We present an encoding of the λµ μ-calculus into the π-calculus. We establish the operational correctness of the encoding, and then we extract from it an abstract machine for the λµ μ-calculus.  ...  We prove that there is a tight relationship between such a machine and Curien and Herbelin's abstract machine for the λµ μ-calculus.  ...  Finally, the symmetry of the calculus suggests that fusion-like calculi might also be interesting target calculi for the encoding. Fig. 1 . 1 Fig. 1.  ... 
doi:10.1007/978-3-642-15640-3_5 fatcat:3tv5xj4v6rh2lf7pxzeodbac3e

Decidability of the restriction equational theory in the partial lambda calculus

Ramón Pino Perez
1989 Theoretical Computer Science  
In his thesis about partiality and A-calculus Eugenio Moggi raised the following conjecture: the equational theory Tr (see definition below) corresponding to the restriction in the partial A-calculus is  ...  Testing the truth of this conjecture is very important because one of the results in Moggi's thesis is the confluence of the partial A-calculus modulo the theory Tr .  ...  We effect a local transformation in the proof 4.  ... 
doi:10.1016/0304-3975(89)90029-7 fatcat:py7fdpvwx5a2vcnbt5rgdmdexe

Page 8225 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
amplitude calculus for processes im- plying instantons.  ...  17B81 8IR10 Park, Mu-In (1-MIT-TP; Cambridge, MA) Symmetry algebras in Chern-Simons theories with boundary: canonical approach.  ... 

2-sphere Schrodinger operators with odd potentials

D Gurarie
1990 Inverse Problems  
We establish local spectral rigidity for odd zonal potentials and give the explicit solution of the inverse spectral problem.  ...  The paper extends our earlier results on spectral theory of the 2-sphere Schrodinger operators H = -A + Vwith even zonal potentials to a more difficult odd-potential case.  ...  Acknowledgments We would like to acknowledge the referee's comments and corrections. This research was partly supported by the US NSF Grant DMS-8620231.  ... 
doi:10.1088/0266-5611/6/3/007 fatcat:kainta6uunbwdmi4j4gaswiqhe

Page 515 of Mathematical Reviews Vol. , Issue 2004a [page]

2004 Mathematical Reviews  
{For the entire collection see MR 2003}:68003. } 2004a:68094 68Q60 68Q85 Mateescu, Radu; Sighireanu, Mihaela (F-PARIS7-FA; Paris) Efficient on-the-fly model-checking for regular alternation-free mu- calculus  ...  Summary: “We present a sequent calculus for formally verifying modal u-calculus properties of concurrent processes.  ... 

Page 3369 of Mathematical Reviews Vol. , Issue 89F [page]

1989 Mathematical Reviews  
The authors state a theorem that relates the theory of dimensional reduction in Hamiltonian mechanics to the spectral properties of elliptic operators with symmetries on compact manifolds.  ...  ., X¥ \ {p} can be put locally in the form R, x M (M a compact Riemannian mani- fold).  ... 

What are symmetries of nonlinear PDEs and what are they themselves? [article]

Alexandre M. Vinogradov
2013 arXiv   pre-print
The general theory of (nonlinear) partial differential equations originated by S. Lie had a significant development in the past 30-40 years.  ...  However, the results of this development are not yet sufficiently known to a wide public.  ...  Additional thanks to Katya Vinogradova for correcting author's "continental English" and to Athanase Papadopoulos for his improving the text suggestions.  ... 
arXiv:1308.5861v1 fatcat:eh6xfj4e2ze6pp2vwsnydysfp4

LTSmin: High-Performance Language-Independent Model Checking [chapter]

Gijs Kant, Alfons Laarman, Jeroen Meijer, Jaco van de Pol, Stefan Blom, Tom van Dijk
2015 Lecture Notes in Computer Science  
reduction, and multi-core symbolic checking for the modal µ-calculus, based on the multi-core decision diagram package Sylvan.  ...  In recent years, the LTSmin model checker has been extended with support for several new modelling languages, including probabilistic (Mapa) and timed systems (Uppaal).  ...  In the future, a symmetry-reduction layer, a la [17] , could implement CoveredBy. Other named matrices, can be added to the generic GetMatrix function, which we label A∞.  ... 
doi:10.1007/978-3-662-46681-0_61 fatcat:zrnithyfxrh4dpyou2mw22axva

The bologna optimal higher-order machine

Andrea Asperti, Cecilia Giovannetti, Andrea Naletto
1996 Journal of functional programming  
The source language is a sugared λ-calculus enriched with booleans, integers, lists and basic operations on these data types (following the guidelines of Interaction Systems – Asperti and Laneve (1993b  ...  AbstractThe Bologna Optimal Higher-order Machine (BOHM) is a prototype implementation of the core of a functional language based on (a variant of) Lamping's optimal graph reduction technique (Lamping,  ...  Optimal Reduction The problem of optimal reduction of the -calculus was defined by J.J. Lévy in [Le78] .  ... 
doi:10.1017/s0956796800001994 fatcat:ht6a57jbvnasla5yn5fozkoose
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