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μ-calculus on data words
[article]
2014
arXiv
pre-print
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We study the decidability and expressiveness issues of 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. ...
arXiv:1404.4827v1
fatcat:2tjm75bsejckbg55t5avsd7cva
Alternation-free modal mu-calculus for data trees
2007
22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
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An alternation-free modal 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. ...
doi:10.1109/lics.2007.11
dblp:conf/lics/JurdzinskiL07
fatcat:yktmtiebqff7zaj2w3xyu3o3fq
Characterizing polynomial and exponential complexity classes in elementary lambda-calculus
2018
Information and Computation
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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-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[µa.S/a] Γ | ∆ | Θ M : µa.S (µI) Γ | ∆ | Θ M : µa.S Γ | ∆ | Θ M : S[µa.S ...
doi:10.1016/j.ic.2018.05.005
fatcat:ycucrc732jfhpbwsjeau6kxlfm
Property Specification Made Easy: Harnessing the Power of Model Checking in UML Designs
[chapter]
2014
Lecture Notes in Computer Science
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Conversely, 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 µcalculus 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. ...
doi:10.1007/978-3-662-43613-4_2
fatcat:xa6rgpnijbeotfsz3sbf32ofwa
The Duality of Construction
[chapter]
2014
Lecture Notes in Computer Science
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The theory may be extended with new logical connectives, in the form of user-defined 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 ...
doi:10.1007/978-3-642-54833-8_14
fatcat:qd5tj3b6kvh3jbfinvfefvk4pi
Formalizing Homogeneous Language Embeddings
2010
Electronical Notes in Theoretical Computer Science
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In this paper we present the 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. ...
doi:10.1016/j.entcs.2010.08.033
fatcat:dwaws53ym5hqlbtgbbgxisn76i
Characterizing Polynomial and Exponential Complexity Classes in Elementary Lambda-Calculus
[chapter]
2014
Lecture Notes in Computer Science
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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-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[μa.S/a] Γ | Δ | Θ M : μa.S (μI) Γ | Δ | Θ M : μa.S Γ | Δ | Θ M : S[μa.S ...
doi:10.1007/978-3-662-44602-7_13
fatcat:iaojnfvgezhdtge7tmbeuuc3vq
Analysing Mu-Calculus Properties of Pushdown Systems
[chapter]
2010
Lecture Notes in Computer Science
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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 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). ...
doi:10.1007/978-3-642-16164-3_14
fatcat:twj6zlwgazd6bo47t5onb6zpue
Combining linear logic and size types for implicit complexity
2019
Theoretical Computer Science
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So 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. ...
doi:10.1016/j.tcs.2019.09.032
fatcat:wbzm7ll2dbe55lenvkvzv2bnqu
Numerical Response Surfaces of Volume of Ablation and Retropulsion Amplitude by Settings of Ho:YAG Laser Lithotripter
2018
Journal of Healthcare Engineering
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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 μs up to 1000 μs. ...
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. ...
doi:10.1155/2018/8261801
pmid:29707187
pmcid:PMC5863310
fatcat:4ziyoptsnvgyjcgo6fnpjtjsnq
Spi calculus translated to /spl pi/-calculus preserving may-tests
2004
Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
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As a consequence, protocols can be described in the spi 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. ...
doi:10.1109/lics.2004.1319597
dblp:conf/lics/BaldamusPV04
fatcat:3sdocx6g7rbzdodtao2gxvuwxe
Structures for structural recursion
2015
SIGPLAN notices
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We also present a more traditional calculus for representing effect-free functional programs, but at the cost of losing some of the founding dualities. 1 Note that symbols µ andμ 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. ...
doi:10.1145/2858949.2784762
fatcat:e3twq6k6hrfq5i2yuqe7qhtps4
Structures for structural recursion
2015
Proceedings of the 20th ACM SIGPLAN International Conference on Functional Programming - ICFP 2015
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We also present a more traditional calculus for representing effect-free functional programs, but at the cost of losing some of the founding dualities. 1 Note that symbols µ andμ 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. ...
doi:10.1145/2784731.2784762
dblp:conf/icfp/DownenJA15
fatcat:4w6762o63jarlnrcqomsexbn3q
Model Checking for String Problems
[chapter]
2014
Lecture Notes in Computer Science
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We consider three computation problems 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. ...
doi:10.1007/978-3-319-06686-8_15
fatcat:tedol2ht7rgchife7lcsxavwfi
Merge Is Not Recursion
2017
Figshare
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The main conclusions are: that the book uses the 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 ...
doi:10.6084/m9.figshare.4958822.v1
fatcat:azo7sp4yt5gddcr6lay4tx574i
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