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Computing special powers in finite fields

Joachim von zur Gathen, Michael Nöcker
2003 Mathematics of Computation  
We study exponentiation in nonprime finite fields with very special exponents such as they occur, for example, in inversion, primitivity tests, and polynomial factorization.  ...  An extended abstract of this paper has been published; see [24] .  ...  We have applied these ideas for addition chains to five computational problems in finite fields: inversion, primitivity testing, and three tasks connected to polynomial factorization. w a(i) = 2 a(i) −  ... 
doi:10.1090/s0025-5718-03-01599-0 fatcat:4t7jhy7canaflfl4v3hxatrstu

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.  ...  the dynamic programming parsing techniques presented in [16] .  ... 
doi:10.1016/b978-1-4832-1313-2.50036-6 dblp:conf/jcdkb/Lang88 fatcat:cglmszdjbzdbxgxdvbui2pfjli

Abstracting abstract control

James Ian Johnson, David Van Horn
2014 Proceedings of the 10th ACM Symposium on Dynamic languages - DLS '14  
We revise the abstracting abstract machines technique to target the stronger computational model of pushdown systems. In place of automata theory, we use only abstract machines and memoization.  ...  The original AAM recipe produces finite state abstractions, which cannot faithfully represent an interpreter's control stack.  ...  ., reflection, computed fields, runtime linking, eval) that all need proper treatment in the abstract.  ... 
doi:10.1145/2661088.2661098 dblp:conf/dls/JohnsonH14 fatcat:jftogwomxjhs3ob62mihglncom

Semantic Essence of AsmL: Extended Abstract [chapter]

Yuri Gurevich, Benjamin Rossman, Wolfram Schulte
2004 Lecture Notes in Computer Science  
The Abstract State Machine Language, AsmL, is a novel executable specification language based on the theory of Abstract State Machines.  ...  In this paper, we explain the design rationale of AsmL and sketch semantics for a kernel of the language. The details will appear in the full version of the paper.  ...  The constructor extends the type map, extends the field map using the corresponding arguments, and returns a fresh object identifier. class A {i as Int} : new A(1).i v −→ 1 (8) Instance fields can immediately  ... 
doi:10.1007/978-3-540-30101-1_11 fatcat:u2yioofwxnfgjiu5uqaxql566e

Extended Abstracts

2010 Cartilage  
Nutraceuticals in the treatment of OA J.  ...  Steinmeyer Giessen/Germany Acknowledgments: This work is supported by the Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science, and the Nakatomi Foundation Research Grant  ...  2007 extended ICRS abstract on the topic.1 The term applies to resurfacing either one unicompartmental knee replacement since the 2007 extended ICRS 22s 22s Extended Abstracts 16.1.1 16.1.1 Biologic  ... 
doi:10.1177/1947603510386038 pmid:26075041 pmcid:PMC4300817 fatcat:m2mv3tnf6vhzndubvwdtltkh5y

Symbolic mathematics system evaluators (extended abstract)

Richard J. Fateman
1996 Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC '96  
Evaluation" of expressions and programs in a computer algebra system is central to every system, but inevitably fails to provide complete satisfaction.  ...  Perhaps in this case, we intend that (modulo 5 3) return "−1 in the finite field Z 3 ".  ...  The operation Power is used in conjunction with the mod operator to provide "special evaluation" facilities: to compute i n mod m where i is an integer, it is undesirable to compute the powering first  ... 
doi:10.1145/236869.236907 dblp:conf/issac/Fateman96 fatcat:bzwdnup5ifh6jjgzcfpsyffy5y

Algorithmic mechanism design (extended abstract)

Noam Nisan, Amir Ronen
1999 Proceedings of the thirty-first annual ACM symposium on Theory of computing - STOC '99  
We also suggest and motivate extensions to the basic model and prove improved upper bounds in the extended model. Many open problems are suggested as well.  ...  Following notions from the field of mechanism design, we suggest a framework for studying such algorithms.  ...  Let us sketch two example applications we have in mind: Load balancing The aggregate power of all computers on the Internet is huge.  ... 
doi:10.1145/301250.301287 dblp:conf/stoc/NisanR99 fatcat:4khbvbrworgvfjd6li3k3rwi4u

Complete geometrical query languages (extended abstract)

Marc Gyssens, Jan Van den Bussche, Dirk Van Gucht
1997 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '97  
We thus extend Chandra and Hare& seminal work on computable queries for relational databases to a spatial setting.  ...  We introduce query languages for spatial databases that are complete, in the sense that they can express precisely all computable queries that are generic with respect to certain classes of transformation8  ...  Note that the language FO[R] fwhile provides full computational power on the natural numbers. We can write a program that builds up relations T (for term) and F (for formula).  ... 
doi:10.1145/263661.263669 dblp:conf/pods/GyssensBG97 fatcat:aisqu75rwzdsvkrmmi7oav4ifq

How to break Gifford's cipher (extended abstract)

Thomas R. Cain, Alan T. Sherman
1994 Proceedings of the 2nd ACM Conference on Computer and communications security - CCS '94  
Applying linear algebra over finite fields, we exploit a time-space tradeoff to separately determine key segments derived from a decomposition of the feedback function.  ...  This work, the first proposed attack on Gifford's cipher, illustrates a powerful attack on stream ciphers and shows that Gifford's cipher is ill-suited for encrypting broadcast data in the MIT-based Boston  ...  All computer work was carried out on workstations at the University of Maryland Baltimore County.  ... 
doi:10.1145/191177.191227 dblp:conf/ccs/CainS94 fatcat:lcpp32olazdjnl4av62jxxvo2i

Process Behaviour: Formulae vs. Tests (Extended Abstract)

Andrea Cerone, Matthew Hennessy
2010 Electronic Proceedings in Theoretical Computer Science  
Then we show that those subsets of the property logic capture precisely the power of tests.  ...  Process behaviour is often defined either in terms of the tests they satisfy, or in terms of the logical properties they enjoy.  ...  Since the LTS generated by s | t is finite branching, we have that the degree of each node in the computation tree above is finite.  ... 
doi:10.4204/eptcs.41.3 fatcat:txsrzb2zoree5lbpjiyx4okq3m

Executable Behaviour and the π-Calculus (extended abstract)

Bas Luttik, Fei Yang
2015 Electronic Proceedings in Theoretical Computer Science  
Reactive Turing machines extend classical Turing machines with a facility to model observable interactive behaviour.  ...  In this paper, we study the relationship between executable behaviour and behaviour that can be specified in the pi-calculus.  ...  We extend D with a special symbol D to denote a blank tape cell, and denote the set D ∪ { } of tape symbols by D . Definition 4.  ... 
doi:10.4204/eptcs.189.5 fatcat:drtj7ymimjcvber7wrlraj7pkm

Overlap properties of geometric expanders: Extended abstract [chapter]

Extended abstract, Jacob Fox, Mikhail Gromov, Vincent Lafforgue, Assaf Naor, János Pach
2011 Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms  
The overlap number of a finite (d + 1)-uniform hypergraph H is the largest constant c(H) ∈ (0, 1] such that no matter how we map the vertices of H into R d , there is a point covered by at least a c(H)  ...  In [18] , motivated by the search for an analogue of the notion of graph expansion for higher dimensional simplicial complexes, it was asked whether or not there exists a sequence {Hn} ∞ n=1 of arbitrarily  ...  Specifically, we show that for every integer r 2, for a large enough odd prime power q, certain finite quotients of the building of P GL r (F ), where F is a non-archimedian local field with residue field  ... 
doi:10.1137/1.9781611973082.90 dblp:conf/soda/FoxGLNP11 fatcat:urwor43p6zfupkiin4beyhev6q

Counting quadrant walks via Tutte's invariant method (extended abstract) [article]

O Bernardi, M Bousquet-Mélou, Kilian Raschel
2016 arXiv   pre-print
Then, we move to an analytic viewpoint which has already proved very powerful, leading in particular to integral expressions of the generating function in the non-D-finite cases, as well as to proofs of  ...  non-D-finiteness.  ...  We are grateful to one of our FPSAC referees who spotted mistakes in our tables.  ... 
arXiv:1511.04298v2 fatcat:yqbfsxe3rrd2xl4t2q4t6wuxua

Generating functions of bipartite maps on orientable surfaces (extended abstract)

Guillaume Chapuy, Wenjie Fang
2015 Discrete Mathematics & Theoretical Computer Science  
However, the present paper requires no previous knowledge of this topic and comes with elementary (complex-analysis-free) proofs written in the perspective of formal power series.  ...  We exhibit an explicit change of variables such that for each $g$, $L$<sub>$g$</sub> is a rational function in the new variables, computable by an explicit recursion on the genus.  ...  If a result cited in this extended abstract is not followed by a proof, this implicitly refers to [CF15] . 2 Surfaces, maps, and the main results Surfaces, maps In this paper, a surface is a connected  ... 
doi:10.46298/dmtcs.2531 fatcat:cpbv5dduxng63dt6l6wfs4u3gi

Functional Encryption for Cascade Automata (Extended Abstract) [chapter]

Dan Brownstein, Shlomi Dolev, Niv Gilboa
2015 Lecture Notes in Computer Science  
As an example of the additional power that a cascade provides, we show a construction of a cascade that accepts a word in a regular language only if it is accompanied by a standard public key signature  ...  Our work extends the work of Waters (Crypto'12) by replacing a single DFA with a cascade.  ...  (grant 428/11), the Israeli Internet Association, and the Ministry of Science and Technology, Infrastructure Research in the Field of Advanced Computing and Cyber Security. function of the plaintext and  ... 
doi:10.1007/978-3-319-21741-3_7 fatcat:kjqeikiscfbhfbe7cq4vkc2g7y
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