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On Finite Alphabets and Infinite Bases II: Completed and Ready Simulation [chapter]

Taolue Chen, Wan Fokkink, Sumit Nain
2006 Lecture Notes in Computer Science  
Furhermore, we prove that with a finite alphabet of actions, the equational theory of BCCSP modulo ready simulation equivalence does not have a finite basis.  ...  In contrast, with an infinite alphabet, the latter equational theory does have a finite basis.  ...  Next we prove that in case of a finite alphabet {b 1 , . . . , b k }, no finite sound and ground-complete axiomatization for BCCSP modulo ready simulation preorder and equivalence is ω-complete.  ... 
doi:10.1007/11690634_1 fatcat:yciu4wcgbffjndd73dcs24orty

On finite alphabets and infinite bases

Taolue Chen, Wan Fokkink, Bas Luttik, Sumit Nain
2008 Information and Computation  
Completed simulation semantics also lacks a finite basis in case of an infinite alphabet of actions.  ...  We prove that in case of a finite alphabet with at least two actions, failure semantics affords a finite basis, while for ready simulation, completed simulation, simulation, possible worlds, ready trace  ...  Acknowledgments We are most grateful to Luca Aceto and Anna Ingolfsdottir for stimulating discussions, and to the anonymous referees for suggesting many improvements.  ... 
doi:10.1016/j.ic.2007.09.003 fatcat:jsmgzz3nanhoxdj5z2y74ymiju

Formalization of a test experiment-II

I. B. Bourdonov, A. S. Kossatchev
2013 Programming and computer software  
In the general model proposed, the dependence between errors may arise when one chooses, as a class of implementations under test, some strict subset of the class of all implemen tations.  ...  The paper is devoted to the problem of dependence between errors defined by specification and to the related problem of optimization of tests.  ...  Note that, for a spec ification based on finite traces, infinite test experi ments add nothing. However, this is not so in the gen eral case.  ... 
doi:10.1134/s0361768813040026 fatcat:h6bn2spzrfdy5meptvoaufqjpq

Revisiting Timed Specification Theory II : Realisability [article]

Chris Chilton, Marta Kwiatkowska, Xu Wang
2013 arXiv   pre-print
Previously, timed concurrent games have been studied in [1,14,13], where one of the key concern is the removal of time-blocking strategies by applying blame assignment [13].  ...  independent development, and quotient for incremental synthesis.  ...  The authors are supported by EU FP7 project CON-NECT, ERC Advanced Grant VERIWARE and EPSRC project EP/F001096.  ... 
arXiv:1304.7590v1 fatcat:bjlhy3gyabbofnq7hbv2tmy6ne

Systolic tree acceptors

Karel Ii Culik, Arto Salomaa, Derick Wood
1984 RAIRO Informatique théorique  
An STA is referred to as binary if: (i) the underlying tree is the complete binary tree, and; (ii) the alphabet of processors, E p , consists of one letter only.  ...  (ii) Synchronization is forced in case of STAs by cutting the given (infinité) tree on a spécifie level.  ... 
doi:10.1051/ita/1984180100531 fatcat:nbsg7ujwq5dunj2ofjx4dm4iea

Automaticity II: Descriptional complexity in the unary case

Carl Pomerance, John Michael Robson, Jeffrey Shallit
1997 Theoretical Computer Science  
Let Z and d be finite alphabets, and let f be a map from C* to A.  ...  Then the deterministic automaticity of f, &(n), is defined to be the size of the minimum finite-state machine that correctly computes f on all inputs of size n -2 log, n -2 log, log, II for almost all  ...  Acknowledgements We would like to acknowledge with thanks the conversations with Eric Bach and Lisa Hellerstein.  ... 
doi:10.1016/s0304-3975(96)00189-2 fatcat:iheoaxtzxvcdffv3uzuz5pfj2i

Implicit automata in typed λ-calculi II: streaming transducers vs categorical semantics [article]

Lê Thành Dũng Nguyên, Camille Noûs, Pierre Pradic
2021 arXiv   pre-print
One direction of this equivalence is proved by encoding copyless streaming string transducers (SSTs), which compute regular functions, into our λ-calculus.  ...  In doing so, we exhibit a connection between a feature of streaming tree transducers and the multiplicative/additive distinction of linear logic.  ...  Acknowledgment We thank Zeinab Galal for her comments on free (co)completions, Sylvain Salvati for discussions on connections between transducers and simply typed λ-calculi, and Gabriel Scherer for his  ... 
arXiv:2008.01050v3 fatcat:ohkq5kyhenbnfimwa54fnu2cji

A Finite Basis for Failure Semantics [chapter]

Wan Fokkink, Sumit Nain
2005 Lecture Notes in Computer Science  
We present a finite ω-complete axiomatization for the process algebra BCCSP modulo failure semantics, in case of a finite alphabet. This solves an open question by Groote [12] .  ...  Other semantics in the spectrum are based on (bi)simulation and on (decorated) traces.  ...  Blom, Fokkink and Nain [4] proved that in case of an infinite alphabet, BCCSP modulo ready trace equivalence does not have a finite (sound and complete) axiomatization.  ... 
doi:10.1007/11523468_61 fatcat:jzscjznxcfczdn7bgj4cxlu4va

On Gödel's Theorems on Lengths of Proofs II: Lower Bounds for Recognizing k Symbol Provability [chapter]

Samuel R. Buss
1995 Feasible Mathematics II  
Gödel's claim is that k -symbol provability in first-order logic can not be decided in o(k) time on a deterministic Turing machine. We prove Gödel's claim and also prove a conjecture of S.  ...  In addition, we prove that the k -symbol provability problem is NP -complete, even for provability in propositional logic.  ...  This widespread belief is based primarily on two facts.  ... 
doi:10.1007/978-1-4612-2566-9_4 fatcat:odt2vy5dabhw7jkhvtqqha2vqa

Divide and congruence II: From decomposition of modal formulas to preservation of delay and weak bisimilarity

Wan Fokkink, Rob van Glabbeek
2017 Information and Computation  
Earlier we presented a method to decompose modal formulas for processes with the internal action τ, and congruence formats for branching and η-bisimilarity were derived on the basis of this decomposition  ...  In this follow-up paper the decomposition method is enhanced to deal with modal characterisations that contain a modality 〈ϵ〉〈 a〉ϕ, to derive congruence formats for delay and weak bisimilarity.  ...  Theorem 3 Let P = (Σ, R) be a delay resistant Γ-patient complete standard TSS in ready simulation format.  ... 
doi:10.1016/j.ic.2017.10.003 fatcat:3gxwy4ttjfeefciysehp5nncie

Relational concurrent refinement part II: Internal operations and outputs

Eerke Boiten, John Derrick, Gerhard Schellhorn
2008 Formal Aspects of Computing  
Acknowledgements We would like to thank Christie Bolton, Jim Davies, Steve Schneider, Helen Treharne and Heike Wehrheim for discussions on these issues, and the anonymous reviewers for their suggestions  ...  and comments.  ...  We do not rely on the conventional assumption that I is finite, and so are not requiring inputs to be from a finite domain either.  ... 
doi:10.1007/s00165-007-0066-z fatcat:bzyo6pdrqvh7xbnwzqfclz6xgu

Finite Equational Bases in Process Algebra: Results and Open Questions [chapter]

Luca Aceto, Wan Fokkink, Anna Ingolfsdottir, Bas Luttik
2005 Lecture Notes in Computer Science  
He studied these semantics in the setting of the basic process algebra BCCSP, and tried to give finite complete and ω-complete axiomatizations for them.  ...  This paper reports on these results, and on the state-of-the-art on axiomatizations for richer process algebras, containing constructs like sequential and parallel composition.  ...  means that it is unknown whether a finite basis exists. We distinguish between an infinite alphabet, a finite alphabet with more than one element, and a singleton alphabet.  ... 
doi:10.1007/11601548_18 fatcat:m4s3gukernajldcolyrzjbqbge

Finite Equational Bases in Process Algebra: Results and Open Questions

Luca Aceto, Willem Jan Fokkink, Anna Ingólfsdóttir, Bas Luttik
2005 BRICS Report Series  
He studied these semantics in the setting of the basic process algebra BCCSP, and tried to give finite complete and omega-complete axiomatizations for them.  ...  This paper reports on these results, and on the state-of-the-art on axiomatizations for richer process algebras, containing constructs like sequential and parallel composition.  ...  means that it is unknown whether a finite basis exists. We distinguish between an infinite alphabet, a finite alphabet with more than one element, and a singleton alphabet.  ... 
doi:10.7146/brics.v12i19.21885 fatcat:qbyvmg3ukvcoha3dremprnhzuu

Rules with parameters in modal logic II [article]

Emil Jeřábek
2020 arXiv   pre-print
We completely classify the complexity of unifiability or inadmissibility in any clx logic as being complete for one of Σ^_2, NEXP, coNEXP, PSPACE, or Π^p_2.  ...  In contrast, our lower bounds are very general: they apply each to a class of all transitive logics whose frames allow occurrence of certain finite subframes.  ...  The universal frame U L (p) consists of two disjoint infinite descending chains alternating between p and ¬p, one with p on top, and the other with ¬p on top.  ... 
arXiv:1905.13157v2 fatcat:e7yxsy5cebf6vebruezshk4eum

The linear time - branching time spectrum [chapter]

R. J. van Glabbeek
1990 Lecture Notes in Computer Science  
Finally nine of these semantics are applied to a simple language for finite, concrete, sequential, nondeterministic processes, and for each of them a complete axiomatization is provided.  ...  Several testing scenarios, motivating these semantics, are presented, phrased in terms of 'button pushing experiments' on generative and reactive machines.  ...  refusal simulation equivalence and coincides with ready simulation equivalence on the domain of finitely branchhag processes.  ... 
doi:10.1007/bfb0039066 fatcat:lgn4pq66rna5pb2vfkcpjcssga
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