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A cut-invariant law of large numbers for random heaps [article]

Samy Abbes
2015 arXiv   pre-print
A notion of cut-invariance is formulated for convergent ergodic means. Then a version of the Strong law of large numbers is proved for heap monoids with Bernoulli measures.  ...  We introduce in this framework the notion of asynchronous stopping time, which is analogous to the notion of stopping time for classical probabilistic processes.  ...  Approximating the root of the Möbius polynomial; 2. Determining the invariant measure of the matrix (17); 3. Computing the speedup through formula (34).  ... 
arXiv:1502.06277v5 fatcat:p4topshzurfz7g6cf4rtfc4rla

A Cut-Invariant Law of Large Numbers for Random Heaps

Samy Abbes
2016 Journal of theoretical probability  
A notion of cut-invariance is formulated for convergent ergodic means. Then, a version of the strong law of large numbers is proved for heap monoids with Bernoulli measures.  ...  We consider the framework of Bernoulli measures for heap monoids.  ...  method allows for robust algorithmic approximation of the speedup, through the following steps: 1.  ... 
doi:10.1007/s10959-016-0692-6 fatcat:ffskrcbcazgknod7rcmod6ausa

Categorical Semantics for Time Travel [article]

Nicola Pinzani, Stefano Gogioso, Bob Coecke
2019 arXiv   pre-print
back in time and provide computational speedups.  ...  Our framework is based on a weakening of the definition of traced symmetric monoidal categories, obtained by dropping the yanking axiom and the requirement that the trace be defined on all morphisms.  ...  In the context of quantum computer science, the possibility of time travel acquires a special significance, because models of quantum processes in the presence of CTCs display large computational speedups  ... 
arXiv:1902.00032v1 fatcat:sh543t6fzvbxfojyleekg5paxi

Uniform and Bernoulli measures on the boundary of trace monoids

Samy Abbes, Jean Mairesse
2015 Journal of combinatorial theory. Series A  
Trace monoids and heaps of pieces appear in various contexts in combinatorics. They also constitute a model used in computer science to describe the executions of asynchronous systems.  ...  In this paper, we introduce and study the class of Bernoulli probability measures that we claim to be the simplest adequate probability measures on infinite traces.  ...  Therefore, the valuation f is not Möbius and q 1 does not qualify to define a uniform measure. 3.2-Computing the speedup In a trace monoid, what is the "average parallelism"?  ... 
doi:10.1016/j.jcta.2015.05.003 fatcat:nxyckx5rlvdcncnksvz666duuq

Synchronization of Bernoulli sequences on shared letters

Samy Abbes
2017 Information and Computation  
We study the probabilistic aspects by considering the synchronization of Bernoulli sequences of letters, under the light of Bernoulli and uniform measures recently introduced for trace monoids.  ...  Synchronizing sequences of letters on alphabets sharing letters are known to produce a trace in the concurrency theoretic sense, i.e., a labeled partially ordered set.  ...  A number of ideas in this paper have emerged through animated discussions with É. Fabre, B. Genest and N. Bertrand at INRIA Rennes during Spring 2015. I am grateful to A.  ... 
doi:10.1016/j.ic.2017.04.002 fatcat:anari6vrerbc3nfbmz754fy6se

The Abstract Structure of Quantum Algorithms [article]

William Zeng
2015 arXiv   pre-print
In the remaining section, we construct a novel model of quantum blackbox algorithms in non-deterministic classical computation. Our second set of results concerns quantum foundations.  ...  The clarity of the process theoretic setting allows us to recover a speedup that is lost in the naive application of the algorithm.  ...  In no way would this have been possible without the dedication, encouragement, and support of many.  ... 
arXiv:1512.08062v1 fatcat:ewzii4cmerghxgysxngokbym3a

Computing the average parallelism in trace monoids

Daniel Krob, Jean Mairesse, Ioannis Michos
2003 Discrete Mathematics  
To illustrate our results and methods, we consider a couple of examples: the free commutative monoid and the trace monoid whose independence graph is the ladder graph.  ...  The height of a trace is the height of the corresponding heap of pieces in Viennot's representation, or equivalently the number of factors in its Cartier-Foata decomposition.  ...  We are also grateful to Alain Jean-Marie for sharing with us his knowledge on the di cult problem of computing * , and to Anne Bouillard for correcting a mistake in an earlier version of the proof of Proposition  ... 
doi:10.1016/s0012-365x(03)00233-4 fatcat:lsm6oqenlbbg7igyn4cf2hjoqq

Semi-local string comparison: algorithmic techniques and applications [article]

Alexander Tiskin
2013 arXiv   pre-print
This work is devoted to exploring the structure of the semi-local LCS problem, its efficient solutions, and its applications in string comparison and other related areas, including computational molecular  ...  Furthermore, the semi-local LCS problem turns out to have surprising connections in a few seemingly unrelated fields, such as computational geometry and algebra of semigroups.  ...  Acknowledgement This work was conceived in a discussion with Gad Landau in Haifa. The imaginative term "seaweeds" was coined by Yuri Matiyasevich during a presentation by the author in St.  ... 
arXiv:0707.3619v21 fatcat:ufmpjbkmsvbvhf6l6zxugdcyc4

A Survey of Quantum Computing for Finance [article]

Dylan Herman, Cody Googin, Xiaoyuan Liu, Alexey Galda, Ilya Safro, Yue Sun, Marco Pistoia, Yuri Alexeev
2022 arXiv   pre-print
In fact, finance is estimated to be the first industry sector to benefit from quantum computing, not only in the medium and long terms, but even in the short term.  ...  We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance.  ...  use cases that lend themselves to quantum computing and their amenability to be solved effectively even in the presence of approximations.  ... 
arXiv:2201.02773v3 fatcat:aqcl6blbyvbljg627ot6zxtaj4

A meta-scheduler for the par-monad

Adam Foltzer, Abhishek Kulkarni, Rebecca Swords, Sajith Sasidharan, Eric Jiang, Ryan Newton
2012 Proceedings of the 17th ACM SIGPLAN international conference on Functional programming - ICFP '12  
Modern parallel computing hardware demands increasingly specialized attention to the details of scheduling and load balancing across heterogeneous execution resources that may include GPU and cloud environments  ...  Many existing solutions address the challenges of particular resources, but do so in isolation, and in general do not compose within larger systems.  ...  Resources, combined with mappend, form a non-commutative monoid so we can compose them using the Monoid type class: 8 instance Monoid Startup instance Monoid WorkSearch instance Monoid Resource The Startup  ... 
doi:10.1145/2364527.2364562 dblp:conf/icfp/FoltzerKSSJN12 fatcat:3huj55wmdrb4bnlsdsuuvthkdu

A meta-scheduler for the par-monad

Adam Foltzer, Abhishek Kulkarni, Rebecca Swords, Sajith Sasidharan, Eric Jiang, Ryan Newton
2012 SIGPLAN notices  
Modern parallel computing hardware demands increasingly specialized attention to the details of scheduling and load balancing across heterogeneous execution resources that may include GPU and cloud environments  ...  Many existing solutions address the challenges of particular resources, but do so in isolation, and in general do not compose within larger systems.  ...  Resources, combined with mappend, form a non-commutative monoid so we can compose them using the Monoid type class: 8 instance Monoid Startup instance Monoid WorkSearch instance Monoid Resource The Startup  ... 
doi:10.1145/2398856.2364562 fatcat:e3ow5h5xbnftlkxhuubwivzmhu

Backprop as Functor: A compositional perspective on supervised learning

Brendan Fong, David Spivak, Remy Tuyeras
2019 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
Further directions Traces and recurrent neural networks In monoidal categories, a structure known as a trace often describes the structure of processes that involve feedback.  ...  In brief, the functoriality means that given two differentiable parametrised functions I and J, we get the same result if we (i) use gradient descent to get learning algorithms for I and J, and then compose  ... 
doi:10.1109/lics.2019.8785665 dblp:conf/lics/FongST19 fatcat:g7btwbi5frfjliyghc4bkiaakq

ENFrame: A Platform for Processing Probabilistic Data [article]

Sebastiaan J. van Schaik and Dan Olteanu and Robert Fink
2013 arXiv   pre-print
We propose an event language that is expressive enough to succinctly encode arbitrary correlations, trace the computation of user programs, and allow for computation of discrete probability distributions  ...  We introduce sequential and distributed algorithms for computing the probability of interconnected events exactly or approximately with error guarantees.  ...  The event language is a non-trivial extension of provenance semirings [16] and semimodules [4] that are used to trace the evaluation of positive relational algebra queries with aggregates and to compute  ... 
arXiv:1309.0373v1 fatcat:mqv5xq53srhgrf4k6hiw2qxnxy

A True Concurrent Model of Smart Contracts Executions [chapter]

Massimo Bartoletti, Letterio Galletta, Maurizio Murgia
2020 Lecture Notes in Computer Science  
the required actions on contracts), and execute them in some order.  ...  Once this sequence of transactions is appended to the blockchain, the other nodes validate it, re-executing the transactions in the same order.  ...  Sardinia projects "Smart collaborative engineering" and "Sardcoin".  ... 
doi:10.1007/978-3-030-50029-0_16 fatcat:wljhlv4uojee5kbaenr2bh7ola

Sigma*

Matko Botinčan, Domagoj Babić
2013 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '13  
By combining dynamic symbolic execution to discover symbolic input-output steps of the programs and counterexample guided abstraction refinement to over-approximate program behavior, Sigma * transforms  ...  Sigma * addresses the challenge of synthesizing models of software by using symbolic conjectures and abstraction.  ...  Acknowledgments This work was supported by the Gates trust, the Lawrence Livermore National Lab grant B597718, and by the NSERC PDF fellowship.  ... 
doi:10.1145/2429069.2429123 dblp:conf/popl/BotincanB13 fatcat:zbozefsolbd3nkybvs6fbeulme
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