98,534 research outputs found
Synthesis observation equivalence and weak synthesis observation equivalence
This working paper proposes an algorithm to simplify automata in such a way that compositional synthesis results are preserved in every possible context. It relaxes some requirements of synthesis observation equivalence from previous work, so that better abstractions can be obtained. The paper describes the algorithm, adapted from known bisimulation equivalence algorithms, for the improved abstraction method. The algorithm has been implemented in the DES software tool Supremica and has been used to compute modular supervisors for several large benchmark examples. It successfully computes modular supervisors for systems with more than 10Ā¹Ā² reachable states
An algorithm for weak synthesis observation equivalence for compositional supervisor synthesis
This paper proposes an algorithm to simplify automata in such a way that compositional synthesis results are preserved in every possible context. It relaxes some requirements of synthesis observation equivalence from previous work, so that better abstractions can be obtained. The paper describes the algorithm, adapted from known bisimulation equivalence algorithms, for the improved abstraction method. The algorithm has been implemented in the DES software tool Supremica and has been used to compute modular supervisors for several large benchmark examples. It successfully computes modular supervisors for systems with more than 1012 reachable states
Testing the Equivalence of Regular Languages
The minimal deterministic finite automaton is generally used to determine
regular languages equality. Antimirov and Mosses proposed a rewrite system for
deciding regular expressions equivalence of which Almeida et al. presented an
improved variant. Hopcroft and Karp proposed an almost linear algorithm for
testing the equivalence of two deterministic finite automata that avoids
minimisation. In this paper we improve the best-case running time, present an
extension of this algorithm to non-deterministic finite automata, and establish
a relationship between this algorithm and the one proposed in Almeida et al. We
also present some experimental comparative results. All these algorithms are
closely related with the recent coalgebraic approach to automata proposed by
Rutten
Faster Convex Optimization: Simulated Annealing with an Efficient Universal Barrier
This paper explores a surprising equivalence between two seemingly-distinct
convex optimization methods. We show that simulated annealing, a well-studied
random walk algorithms, is directly equivalent, in a certain sense, to the
central path interior point algorithm for the the entropic universal barrier
function. This connection exhibits several benefits. First, we are able improve
the state of the art time complexity for convex optimization under the
membership oracle model. We improve the analysis of the randomized algorithm of
Kalai and Vempala by utilizing tools developed by Nesterov and Nemirovskii that
underly the central path following interior point algorithm. We are able to
tighten the temperature schedule for simulated annealing which gives an
improved running time, reducing by square root of the dimension in certain
instances. Second, we get an efficient randomized interior point method with an
efficiently computable universal barrier for any convex set described by a
membership oracle. Previously, efficiently computable barriers were known only
for particular convex sets
An Improved Affine Equivalence Algorithm for Random Permutations
In this paper we study the affine equivalence problem, where given two functions , the goal is to determine whether there exist invertible affine transformations over such that . Algorithms for this problem have several well-known applications in the design and analysis of Sboxes, cryptanalysis of white-box ciphers and breaking a generalized Even-Mansour scheme.
We describe a new algorithm for the affine equivalence problem and focus on the variant where are permutations over -bit words, as it has the widest applicability. The complexity of our algorithm is about bit operations with very high probability whenever (or is a random permutation. This improves upon the best known algorithms for this problem (published by Biryukov et al. at EUROCRYPT 2003), where the first algorithm has time complexity of and the second has time complexity of about and roughly the same memory complexity.
Our algorithm is based on a new structure (called a \emph{rank table}) which is used to analyze particular algebraic properties of a function that remain invariant under invertible affine transformations. Besides its standard application in our new algorithm, the rank table is of independent interest and we discuss several of its additional potential applications
On Similarities between Inference in Game Theory and Machine Learning
In this paper, we elucidate the equivalence between inference in game theory and machine learning. Our aim in so doing is to establish an equivalent vocabulary between the two domains so as to facilitate developments at the intersection of both fields, and as proof of the usefulness of this approach, we use recent developments in each field to make useful improvements to the other. More specifically, we consider the analogies between smooth best responses in fictitious play and Bayesian inference methods. Initially, we use these insights to develop and demonstrate an improved algorithm for learning in games based on probabilistic moderation. That is, by integrating over the distribution of opponent strategies (a Bayesian approach within machine learning) rather than taking a simple empirical average (the approach used in standard fictitious play) we derive a novel moderated fictitious play algorithm and show that it is more likely than standard fictitious play to converge to a payoff-dominant but risk-dominated Nash equilibrium in a simple coordination game. Furthermore we consider the converse case, and show how insights from game theory can be used to derive two improved mean field variational learning algorithms. We first show that the standard update rule of mean field variational learning is analogous to a Cournot adjustment within game theory. By analogy with fictitious play, we then suggest an improved update rule, and show that this results in fictitious variational play, an improved mean field variational learning algorithm that exhibits better convergence in highly or strongly connected graphical models. Second, we use a recent advance in fictitious play, namely dynamic fictitious play, to derive a derivative action variational learning algorithm, that exhibits superior convergence properties on a canonical machine learning problem (clustering a mixture distribution)
Construction of nice nilpotent Lie groups
We illustrate an algorithm to classify nice nilpotent Lie algebras of
dimension up to a suitable notion of equivalence; applying the algorithm,
we obtain complete listings for . On every nilpotent Lie algebra of
dimension , we determine the number of inequivalent nice bases, which
can be , , or .
We show that any nilpotent Lie algebra of dimension has at most countably
many inequivalent nice bases.Comment: v3: Condition (N3) has been changed to exclude diagrams with arrows
with the same label as the starting node, this will not affect the rest of
the paper or the results, since this condition was implicitly assumed through
the paper. Added a final remark 3.9. Presentation improved and bibliography
updated. Article 28 Pages; Tables in ancillary file 137 page
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