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Finitary semantics of linear logic and higher-order model-checking [article]

Charles Grellois, Paul-André Melliès
2015 arXiv   pre-print
The main idea is to start from an infinitary and colored relational semantics of the lambdaY-calculus already formulated, and to replace it by its finitary counterpart based on finite prime-algebraic lattices  ...  In this paper, we explain how the connection between higher-order model-checking and linear logic recently exhibited by the authors leads to a new and conceptually enlightening proof of the selection problem  ...  Future work includes a detailed comparison with a similar line of work on finite models of the λ Y -calculus currently developed by Salvati and Walukiewicz [10] .  ... 
arXiv:1502.05147v2 fatcat:lseygm2skzcorilqj7s7o55n4m

Reducing Higher-order Recursion Scheme Equivalence to Coinductive Higher-order Constrained Horn Clauses

Jerome Jochems
2021 Electronic Proceedings in Theoretical Computer Science  
Correctness of this encoding reduces decidability of the open HoRS equivalence problem -- and, thus, the LambdaY-calculus B\"ohm tree equivalence problem -- to semi-decidability of coinductive HoCHC over  ...  Thus, s is an upper bound on D. However, D is the least upper bound on this set, so D ⊑ s.  ...  Although HoRS are programs of a simply-typed λ Y-calculus, constructed from uninterpreted function symbols, they define a strict subsystem of the λ Y-calculus: the same set of trees as ground-type λ Y-terms  ... 
doi:10.4204/eptcs.344.4 fatcat:pufqgwo65vax5c7tzrz32mlzue

An increasing variables singular system of fractional q-differential equations via numerical calculations

Mohammad Esmael Samei, Dumitru Baleanu, Shahram Rezapour
2020 Advances in Difference Equations  
We investigate the existence of solutions for an increasing variables singular m-dimensional system of fractional q-differential equations on a time scale.  ...  In this singular system, the first equation has two variables and the number of variables increases permanently.  ...  Acknowledgements The first author was supported by Bu Ali Sina Uinversity. The third author was supported by Azarbaijan Shahid Madani University. Funding Not applicable.  ... 
doi:10.1186/s13662-020-02913-5 fatcat:fvo2dqruojggbbdagq34g3eex4

Report from Dagstuhl Seminar 14141 Reachability Problems for Infinite-State Systems

Javier Esparza, Alain Finkel, Pierre Mckenzie, Joel Ouaknine, Javier Esparza, Alain Finkel, Pierre Mckenzie, Joel Ouaknine, Javier Esparza, Alain Finkel, Pierre Mckenzie, Joel Ouaknine (+1 others)
The seminar focussed on complexity and algorithmic issues for the verification of infinite-state systems, with special emphasis on reachability problems.  ...  If zero-tests are allowed-one speaks of "Minsky machines"-, counter systems have the power of Turing machines, and so all their verification problems  ...  LambdaY-calculus is simply typed lambda calculus with fixpoint operators. This calculus faithfully models control in higher-order programs.  ... 

James Joseph Sylvester

M. Noether
1898 Mathematische Annalen  
Oct. 1851 ; in diesen beiden Noten werden auch die Namen ,In-" und ,,Oovariante" zum ersten Male vorgeschlagen und eingeffihrt; besonders: ,On the calculus of forms, otherwise the theory of invariants"  ...  of the second ordre" und ,,On the relation between the minor determinants of linearly equivalent quadratic forms".  ... 
doi:10.1007/bf01444441 fatcat:h7as6dtkvnflpkdoj3anurc7am

NITROGEN, Numerical and Iterative Techniques for Rovibronic Energies with General Internal Coordinates, version 1.10 [article]

P. Bryan Changala
2020 Zenodo  
The reaction path We now introduce the reaction path r µ (s), where s is the reaction path coordinate.  ...  Let σ µ = ∂ s r µ , the direction of the reaction path at s. r µ (s) has the following properties:  ...  The desired eigenpair of which to calculate derivatives is specified by the index I (0-indexed). The results are returned in lambdaI and VI.  ... 
doi:10.5281/zenodo.4288924 fatcat:qmwjmg7wjffmlev2vsl5br6ws4

Experimental study and computational modelling of the biomechanical properties of arteries

Chen Yen Ooi, Apollo-University Of Cambridge Repository, Apollo-University Of Cambridge Repository
The study on the biomechanics of atherosclerotic arteries was then extended to the muscle active properties of the diseased vessels.  ...  The optical flow technique was then used on the analysis of the images obtained from the experiments of human coronary arteries with atherosclerosis.  ...  Using the calculus of variation and the approximation to the Laplacian to solve for u and v, the following equations are obtained: ( ) ( ) ̅ ̅ ( ) ( ) ̅ ̅ (2.6) where ̅ and ̅ are the weighted average of  ... 
doi:10.17863/cam.14095 fatcat:i5s5ab5bhreyll6edzyptnir6a

Implementation funktionaler Programmiersprachen durch Quelltexttransformation [article]

Dragan Macos, Humboldt-Universität Zu Berlin, Humboldt-Universität Zu Berlin
The analyzed techniques cover both classes of functional languages, strict and non-strict ones.  ...  In the first part, we give a formal definition for translating a simple functional language (syntacticly sugared lambda calculus) into the code of a procedural programming language.  ...  In the rst part, we give a formal de nition for translating a simple functional language syntactic sugared lambda calculus into the code of a procedural programming language.  ... 
doi:10.18452/14353 fatcat:s23es5oblna2jadmesvw3urslm