相关论文: A Recursive Definition of the Holographic Standard…

The theory of holographic algorithms, which are polynomial time algorithms for certain combinatorial counting problems, yields insight into the hierarchy of complexity classes. In particular, the theory produces algebraic tests for a…

A holographic algorithm solves a problem in domain of size $n$, by reducing it to counting perfect matchings in planar graphs. It may simulate a $n$-value variable by a bunch of $t$ matchgate bits, which has $2^t$ values. The transformation…

An essential problem in the design of holographic algorithms is to decide whether the required signatures can be realized by matchgates under a suitable basis transformation (SRP). For holographic algorithms on domain size 2, [1, 2, 4, 5]…

Holographic algorithms introduced by Valiant are composed of two ingredients: matchgates, which are gadgets realizing local constraint functions by weighted planar perfect matchings, and holographic reductions, which show equivalences among…

In this article we introduce the insertion method for reconstructing the path from its signature, i.e. inverting the signature of a path. For this purpose, we prove that a converging upper bound exists for the difference between the…

I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…

Signed graphs are studied since the middle of the last century. Recently, the notion of homomorphism of signed graphs has been introduced since this notion captures a number of well known conjectures which can be reformulated using the…

The size of a probe bead reported by holographic particle characterization depends on the proportion of the surface area covered by bound target molecules and so can be used as an assay for molecular binding. We validate this technique by…

Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…

Valiant introduced matchgate computation and holographic algorithms. A number of seemingly exponential time problems can be solved by this novel algorithmic paradigm in polynomial time. We show that, in a very strong sense, matchgate…

In this article, we give a sufficient and necessary condition for determining whether a matchgate signature retains its property under a certain variable permutation, which can be checked in polynomial time. We also define the concept of…

This paper proposes three measures to quantify the characteristics of online signature templates in terms of distinctiveness, complexity and repeatability. A distinctiveness measure of a signature template is computed from a set of enrolled…

In this paper we propose an identification procedure of a sparse graphical model associated to a Gaussian stationary stochastic process. The identification paradigm exploits the approximation of autoregressive processes through reciprocal…

Splines are central objects for the interpolation of discrete data via piecewise smooth paths. Their iterated-integral signature is an infinite collection of tensors which characterizes paths almost uniquely. We study truncations of this…

Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…

In multimedia, text or bioinformatics databases, applications query sequences of n consecutive symbols called n-grams. Estimating the number of distinct n-grams is a view-size estimation problem. While view sizes can be estimated by…

We propose randomized frameproof codes for content protection, which arise by studying a variation of the Boneh-Shaw fingerprinting problem. In the modified system, whenever a user tries to access his fingerprinted copy, the fingerprint is…

This paper presents a recursive hiding scheme for 2 out of 3 secret sharing. In recursive hiding of secrets, the user encodes additional information about smaller secrets in the shares of a larger secret without an expansion in the size of…

We consider recursive decoding techniques for RM codes, their subcodes, and newly designed codes. For moderate lengths up to 512, we obtain near-optimum decoding with feasible complexity.

We present a recursive formulation of the Horn algorithm for deciding the satisfiability of propositional clauses. The usual presentations in imperative pseudo-code are informal and not suitable for simple proofs of its main properties. By…