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μ-calculus on data words
[article]

2014
*
arXiv
*
pre-print

We study the decidability and expressiveness issues of

arXiv:1404.4827v1
fatcat:2tjm75bsejckbg55t5avsd7cva
*μ*-*calculus**on**data**words*and*data*ω-*words*. ... Furthermore,*Data*-LTL and two-variable first-order logic are expressed as unary alternation-free fragment of BMA. Finally basic inclusions of the fragments are discussed. ...*µ*-*Calculus**on**Data**Words*In this section, we introduce*µ*-*calculus*over*data**words*and*data*ω-*words*and establish the basic decidability results. ...##
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Alternation-free modal mu-calculus for data trees

2007
*
22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
*

An alternation-free modal

doi:10.1109/lics.2007.11
dblp:conf/lics/JurdzinskiL07
fatcat:yktmtiebqff7zaj2w3xyu3o3fq
*µ*-*calculus*over*data*trees is introduced and studied. ... The paper shows that, for reasoning about*data*trees, the forward fragment of the*calculus*with*one*register is a powerful alternative to a recently proposed first-order logic with two variables. ... A*data**word*is a*word*over a finite alphabet, with an equivalence relation*on**word*positions. ...##
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Characterizing polynomial and exponential complexity classes in elementary lambda-calculus

2018
*
Information and Computation
*

In this paper an implicit characterization of the complexity classes k-EXP and k-FEXP, for k ≥ 0, is given, by a type assignment system for a stratified λ-

doi:10.1016/j.ic.2018.05.005
fatcat:ycucrc732jfhpbwsjeau6kxlfm
*calculus*, where types for programs are witnesses ... k D, where k ∈ N and D is*one*of the*data*representations above. ... Γ | ∆ | Θ M : S a ∈ FTV(Γ ) ∪ FTV(∆) ∪ FTV(Θ) Γ | ∆ | Θ M : ∀a.S (∀I) Γ | ∆ | Θ M : ∀a.S Γ | ∆ | Θ M : S[σ/a] (∀E) Γ | ∆ | Θ M : S[*µ*a.S/a] Γ | ∆ | Θ M :*µ*a.S (*µ*I) Γ | ∆ | Θ M :*µ*a.S Γ | ∆ | Θ M : S[*µ*a.S ...##
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Property Specification Made Easy: Harnessing the Power of Model Checking in UML Designs
[chapter]

2014
*
Lecture Notes in Computer Science
*

Conversely,

doi:10.1007/978-3-662-43613-4_2
fatcat:xa6rgpnijbeotfsz3sbf32ofwa
*µ*-*calculus*is event-based, making it a good match for sequence diagrams, where communication between components is depicted. ... PASS instantiates pattern templates using three notations: a natural language summary, a*µ**calculus*formula and a UML sequence diagram depicting the desired behavior. ... We utilized mCRL2's rich*data*extensions of the*μ*-*calculus*to express complex*data*-dependent properties. ...##
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The Duality of Construction
[chapter]

2014
*
Lecture Notes in Computer Science
*

The theory may be extended with new logical connectives, in the form of user-defined

doi:10.1007/978-3-642-54833-8_14
fatcat:qd5tj3b6kvh3jbfinvfefvk4pi
*data*and co-*data*types, which are duals of*one*another. ... Finally, we explore a*calculus*with composite evaluation strategies that allow for more flexibility over evaluation order by mingling multiple primitive strategies within a single program. ... In other*words*, a strategy is identified by a choice of values and co-values. (2) We enrich the sequent*calculus*with user-defined*data*and co-*data*types, whose behavior are defined exclusively in terms ...##
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Formalizing Homogeneous Language Embeddings

2010
*
Electronical Notes in Theoretical Computer Science
*

In this paper we present the

doi:10.1016/j.entcs.2010.08.033
fatcat:dwaws53ym5hqlbtgbbgxisn76i
*µ*-*calculus*which allows parameterisable language embeddings to be specified and analysed. ... Conclusions In this paper we defined the*µ*-*calculus*which allows languages and homogeneous language embeddings to be specified. ... We finally showed how the*µ*-*calculus*can be used to specify how DSLs such as an HTML generation language and SQL can be embedded within each other. ...##
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Characterizing Polynomial and Exponential Complexity Classes in Elementary Lambda-Calculus
[chapter]

2014
*
Lecture Notes in Computer Science
*

In this paper an implicit characterization of the complexity classes k-EXP and k-FEXP, for k ≥ 0, is given, by a type assignment system for a stratified λ-

doi:10.1007/978-3-662-44602-7_13
fatcat:iaojnfvgezhdtge7tmbeuuc3vq
*calculus*, where types for programs are witnesses ... k D, where k ∈ N and D is*one*of the*data*representations above. ... Γ | Δ | Θ M : S a ∈ FTV(Γ ) ∪ FTV(Δ) ∪ FTV(Θ) Γ | Δ | Θ M : ∀a.S (∀I) Γ | Δ | Θ M : ∀a.S Γ | Δ | Θ M : S[σ/a] (∀E) Γ | Δ | Θ M : S[*μ*a.S/a] Γ | Δ | Θ M :*μ*a.S (*μ*I) Γ | Δ | Θ M :*μ*a.S Γ | Δ | Θ M : S[*μ*a.S ...##
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Analysing Mu-Calculus Properties of Pushdown Systems
[chapter]

2010
*
Lecture Notes in Computer Science
*

We provide a tool (PDSolver) implementing an algorithm for computing the winning regions of a pushdown parity game and its adaptation to the direct computation of modal

doi:10.1007/978-3-642-16164-3_14
fatcat:twj6zlwgazd6bo47t5onb6zpue
*µ*-*calculus*properties over pushdown ... Secondly, we use the tool to perform dataflow analysis*on*real-world Java programs, taken from the DaCapo benchmark suite. ... The modal*µ*-*calculus*is a highly expressive specification language (subsuming all standard temporal logics). ...##
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Combining linear logic and size types for implicit complexity

2019
*
Theoretical Computer Science
*

So

doi:10.1016/j.tcs.2019.09.032
fatcat:wbzm7ll2dbe55lenvkvzv2bnqu
*on*the*one*hand level-based systems manage higherorder but have a poor expressivity, and*on*the other hand sized-based systems have a good expressivity but do not characterize complexity classes within ... Our system is based*on*elementary linear logic combined with linear size types, called sEAL, and leads to characterizations of the complexity classes FPTIME and 2k-FEXPTIME, for k >= 0. complexity*one*... Those examples show that this*calculus*suffers from limitation. First, we need to work with Church integers, because of a lack of*data*structure. ...##
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Numerical Response Surfaces of Volume of Ablation and Retropulsion Amplitude by Settings of Ho:YAG Laser Lithotripter

2018
*
Journal of Healthcare Engineering
*

A lab-built Ho:YAG laser was used as the laser pulse source, with a pulse energy from 0.2 J up to 3.0 J and a pulse width of 150

doi:10.1155/2018/8261801
pmid:29707187
pmcid:PMC5863310
fatcat:4ziyoptsnvgyjcgo6fnpjtjsnq
*μ*s up to 1000*μ*s. ... The aim of this study was to look for quantitative responses of*calculus*ablation and retropulsion by performing operator-independent experiments to determine the best fit versus the pulse energy, pulse ... In other*words*, ablation decreases faster than retropulsion by increasing pulse length. ...##
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Spi calculus translated to /spl pi/-calculus preserving may-tests

2004
*
Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
*

As a consequence, protocols can be described in the spi

doi:10.1109/lics.2004.1319597
dblp:conf/lics/BaldamusPV04
fatcat:3sdocx6g7rbzdodtao2gxvuwxe
*calculus*and analysed with the emerging flora of tools already available for . ... We present a concise and natural encoding of the spicalculus into the more basic -*calculus*and establish its correctness with respect to a formal notion of testing. ... In other*words*, we establish that cryptography can be encoded into the -*calculus*along standard lines of encoding functions and*data*structures. ...##
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Structures for structural recursion

2015
*
SIGPLAN notices
*

We also present a more traditional

doi:10.1145/2858949.2784762
fatcat:e3twq6k6hrfq5i2yuqe7qhtps4
*calculus*for representing effect-free functional programs, but at the cost of losing some of the founding dualities. 1 Note that symbols*µ*and*μ*used here are not related ... and co-*data*types. ... Acknowledgments We would like to thank the anonymous reviewers for their helpful feedback*on*improving this paper. Paul Downen and Zena M. Ariola have been supported by NSF grant CCF-1423617. ...##
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Structures for structural recursion

2015
*
Proceedings of the 20th ACM SIGPLAN International Conference on Functional Programming - ICFP 2015
*

We also present a more traditional

doi:10.1145/2784731.2784762
dblp:conf/icfp/DownenJA15
fatcat:4w6762o63jarlnrcqomsexbn3q
*calculus*for representing effect-free functional programs, but at the cost of losing some of the founding dualities. 1 Note that symbols*µ*and*μ*used here are not related ... and co-*data*types. ... Acknowledgments We would like to thank the anonymous reviewers for their helpful feedback*on*improving this paper. Paul Downen and Zena M. Ariola have been supported by NSF grant CCF-1423617. ...##
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Model Checking for String Problems
[chapter]

2014
*
Lecture Notes in Computer Science
*

We consider three computation problems

doi:10.1007/978-3-319-06686-8_15
fatcat:tedol2ht7rgchife7lcsxavwfi
*on*strings and show how the polyadic modal*µ*-*calculus*can define their solutions. ... We use partial evaluation*on*a model checking algorithm in order to obtain an efficient algorithm for the longest common substring problem. ...*µ*-*calculus*. ...##
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Merge Is Not Recursion

2017
*
Figshare
*

The main conclusions are: that the book uses the

doi:10.6084/m9.figshare.4958822.v1
fatcat:azo7sp4yt5gddcr6lay4tx574i
*word*"recursion" with a meaning that does not correspond to the meaning used in mathematics, causing confusion, and that the theory proposed in the book ... We can call it lambda-mu-*calculus*, and it is, except*on*its syntax, identical to lambda-*calculus*. ¶5 • In lambda-*calculus*, cons is the operation that builds composed*data*structures, just as Merge is in ...*one*as input*data*(the program). ¶3 • Therefore, the sentence can be corrected just by adding*one**word*, universal, thus: "Consider a universal Turing machine, which after all ought to be able to carry ...
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