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Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond [article]

Thomas H. Gibson, Lawrence Mitchell, David A. Ham, Colin J. Cotter
2019 arXiv   pre-print
We provide examples derived from second order elliptic problems and geophysical fluid dynamics.  ...  In this paper, we introduce a domain-specific abstraction within the Firedrake finite element library that permits the rapid execution of these hybridization techniques within a code-generating framework  ...  The form a(c; v) describes a finite element form globally over the entire problem domain.  ... 
arXiv:1802.00303v4 fatcat:jpeqzk2ztjh2nor62oqwgy7p2u

Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond

Thomas H. Gibson, Lawrence Mitchell, David A. Ham, Colin J. Cotter
2019 Geoscientific Model Development Discussions  
We provide examples derived from second order elliptic problems and geophysical fluid dynamics.  ...  In this paper, we introduce a domain-specific abstraction within the Firedrake finite element library that permits the rapid execution of these hybridization techniques within a code-generating framework  ...  The form a(c; v) describes a finite element form globally over the entire problem domain.  ... 
doi:10.5194/gmd-2019-86 fatcat:kk7uhcn3v5e3ngg4pgo2eukbk4

Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond

Thomas H. Gibson, Lawrence Mitchell, David A. Ham, Colin J. Cotter
2020 Geoscientific Model Development  
We provide examples derived from second-order elliptic problems and geophysical fluid dynamics.  ...  In this paper, we introduce a domain-specific abstraction within the Firedrake finite element library that permits the rapid execution of these hybridization techniques within a code-generating framework  ...  McRae for providing thoughtful comments on early drafts of this paper. Financial support. This research has been supported by the Engineering and Physical Sciences Research Council (grant nos.  ... 
doi:10.5194/gmd-13-735-2020 fatcat:b6bms3wjavca5mvgy72qwqwb3e

Datalog Automata Extended Abstract [chapter]

Bernard LANG
1988 Proceedings of the Third International Conference on Data and Knowledge Bases  
By extending to these automata a dynamic programming technique developed for PDAs in context-free parsing, we obtain a general and simple technique for constructing efficient polynomial query evaluators  ...  We propose a new computational paradigm for the evaluation of recursive Datalog queries, which is based on a pushdown automaton (PDA) model.  ...  work [39] , while the author's current research interest was on extending the dynamic programming parsing techniques presented in [16] .  ... 
doi:10.1016/b978-1-4832-1313-2.50036-6 dblp:conf/jcdkb/Lang88 fatcat:cglmszdjbzdbxgxdvbui2pfjli

Symbolic mathematics system evaluators (extended abstract)

Richard J. Fateman
1996 Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC '96  
The notation and semantics of the CAS should be suitable for algorithmic programming, as well as (several levels) of description of mathematical objects, ranging from the abstract to the relatively concrete  ...  Then note that the context of (modulo 5 3) affects the constraint on (* 2 2), because we now presume that the + is addition over a finite field.  ...  Using the fixed-point philosophy throughout the system (not just at command level as in Maple) requires Mathematica to efficiently determine that when a rule is attempted, no change has in fact happened  ... 
doi:10.1145/236869.236907 dblp:conf/issac/Fateman96 fatcat:bzwdnup5ifh6jjgzcfpsyffy5y

Identifying Shapes Using Self-Assembly (extended abstract) [article]

Matthew J. Patitz, Scott M. Summers
2010 arXiv   pre-print
In this paper, we introduce the following problem in the theory of algorithmic self-assembly: given an input shape as the seed of a tile-based self-assembly system, design a finite tile set that can, in  ...  Acknowledgments Both authors would like to thank Paul Rothemund and John Mayfield for helpful discussions and useful feedback.  ...  Informal Description of the Two-Handed Abstract Tile Assembly Model In this subsection we informally review a variant of Erik Winfree's abstract Tile Assembly Model [29, 30] modified to model unseeded  ... 
arXiv:1006.3046v1 fatcat:kqs4lykx4ngnzlivjcjhevav6e

Unbounded-Time Analysis of Guarded LTI Systems with Inputs by Abstract Acceleration (extended version) [article]

Dario Cattaruzza, Alessandro Abate, Peter Schrammel, Daniel Kroening
2017 arXiv   pre-print
To tackle this problem, we use abstract acceleration, a method for unbounded-time polyhedral reachability analysis for linear systems.  ...  Our experiments show that performance increases by several orders of magnitude over alternative approaches in the literature.  ...  At the time of writing, there are two algorithms that efficiently solve the vertex enumeration problem. lrs is a reverse search algorithm, while cdd follows the double description method.  ... 
arXiv:1506.05607v5 fatcat:bkek7tbrcnemvibj5y4pvmnfia

Client-Server Password Recovery (Extended Abstract) [article]

Łukasz Chmielewski, Jaap-Henk Hoepman, Peter van Rossum
2009 arXiv   pre-print
One example is forgetting a password, a common problem raised at IT help desks.  ...  Conclusions In this paper we have presented secure and efficient solutions for password recovery, where the recovery data is stored securely at the server side.  ...  Let G =<g> denote a finite cyclic (multiplicative) group of prime order q for which the Decision Diffie-Hellman (DDH) problem is assumed to be infeasible: given g α , g β , g γ , where either g γ ∈ R G  ... 
arXiv:0906.4668v1 fatcat:yy5zj6ofyng5bogt3j2xovwsy4

Lost in Abstraction: Monotonicity in Multi-Threaded Programs (Extended Technical Report) [article]

Alexander Kaiser, Daniel Kroening, Thomas Wahl
2014 arXiv   pre-print
In this paper, we show that the act of obtaining finite-data thread abstractions for model checking can be at odds with monotonicity: Predicate-abstracting certain widely used monotone software results  ...  As a result, well-established sound and complete safety checking algorithms become inapplicable; in fact, safety checking turns out to be undecidable for the obtained class of unbounded-thread Boolean  ...  This strategy turns out to be wrong: the full class of Boolean DR programs is expressive enough to render safety checking for an unbounded number of threads undecidable, despite the finite-domain variables  ... 
arXiv:1406.5715v2 fatcat:necrlavcqvhujblmquutt5x3dq

Model Sketching by Abstraction Refinement for Lifted Model Checking (Extended Version) [article]

Aleksandar S. Dimovski
2021 arXiv   pre-print
In particular, we present an approach for synthesizing Promela model sketches using variability-specific abstraction refinement for lifted (family-based) model checking.  ...  In this work, we show how the use of verification and analysis techniques for model families (software product lines) with numerical features provides an interesting technique to synthesize complete models  ...  Several lifted abstract domains for static analysis of numerical program families. Sci. Comput.  ... 
arXiv:2112.11546v1 fatcat:7wsqdmsunrecpdvq5uhnnav52m

The complexity of approximations for epistemic synthesis (extended abstract)

Xiaowei Huang, Ron van der Meyden
2016 Electronic Proceedings in Theoretical Computer Science  
A number of ways to construct such approximations is considered, and these are studied for the complexity of the associated model checking problems.  ...  The paper proposes an approach to the synthesis of implementations of epistemic protocol specifications, that reduces the problem of finding an implementation to a sequence of model checking problems in  ...  states, so the algorithm for I also resolves these cases.  ... 
doi:10.4204/eptcs.202.9 fatcat:3imrfjznsrbtfpbqfbdcgicsoe

Complex Functional Rates in the Modeling of Nano Devices (Extended Abstract)

Cristian Versari, Gianluigi Zavattaro
2013 Electronical Notes in Theoretical Computer Science  
Nevertheless, there are fragments of Kappa for which this problem turns out to be decidable [17] , and also techniques -based on abstract interpretation-which are capable of computing an over-approximation  ...  algorithms.  ... 
doi:10.1016/j.entcs.2013.02.015 fatcat:ruzfia2wrfh5hlifs2somfgddi

The octahedron abstract domain

Robert Clarisó, Jordi Cortadella
2007 Science of Computer Programming  
The contribution of this paper is a new numerical abstract domain called octahedron that represents constraints of the form ( x i − x j ≥ k).  ...  Complex properties can be analyzed using abstract interpretation, provided that an adequate abstract domain is defined.  ...  Acknowledgements The authors would like to thank the referees for their insightful comments which have enhanced the final version of this paper.  ... 
doi:10.1016/j.scico.2006.03.009 fatcat:dzfammxc2fb53n2bjx57mzkf34

The Octahedron Abstract Domain [chapter]

Robert Clarisó, Jordi Cortadella
2004 Lecture Notes in Computer Science  
The contribution of this paper is a new numerical abstract domain called octahedron that represents constraints of the form ( x i − x j ≥ k).  ...  Complex properties can be analyzed using abstract interpretation, provided that an adequate abstract domain is defined.  ...  Acknowledgements The authors would like to thank the referees for their insightful comments which have enhanced the final version of this paper.  ... 
doi:10.1007/978-3-540-27864-1_23 fatcat:xc3r2sdyl5hmzazycuxrt33rba

A Constraint Solver Based on Abstract Domains [chapter]

Marie Pelleau, Antoine Miné, Charlotte Truchet, Frédéric Benhamou
2013 Lecture Notes in Computer Science  
In this article, we apply techniques from Abstract Interpretation (a general theory of semantic abstractions) to Constraint Programming (which aims at solving hard combinatorial problems with a generic  ...  can be mapped to non-relational abstract domains.  ...  We now consider the abstract domain E = P finite (D ), and equip it with the Smyth order E , a classic order for disjunctive completions defined as: X E Y ⇐⇒ ∀B ∈ X , ∃C ∈ Y , B C The creation of new disjunctions  ... 
doi:10.1007/978-3-642-35873-9_26 fatcat:xi6f7hdayrgfnoppwgslidksb4
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