Related papers: On Holant Theorem and Its Proof
The Holant theorem is a powerful tool for studying the computational complexity of counting problems in the Holant framework. Due to the great expressiveness of the Holant framework, a converse to the Holant theorem would itself be a very…
This paper stands at the intersection of two distinct lines of research. One line is "holographic algorithms," a powerful approach introduced by Valiant for solving various counting problems in computer science; the other is "normal factor…
Holant problems are a framework for the analysis of counting complexity problems on graphs. This framework is simultaneously general enough to encompass many other counting problems on graphs and specific enough to allow the derivation of…
Holant problems are a family of counting problems parameterised by sets of algebraic-complex valued constraint functions, and defined on graphs. They arise from the theory of holographic algorithms, which was originally inspired by concepts…
Valiant's Holant theorem is a powerful tool for algorithms and reductions for counting problems. It states that if two sets $\mathcal{F}$ and $\mathcal{G}$ of tensors (a.k.a. constraint functions or signatures) are related by a…
We explore the intricate interdependent relationship among counting problems, considered from three frameworks for such problems: Holant Problems, counting CSP and weighted H-colorings. We consider these problems for general complex valued…
Holant problems capture a class of Sum-of-Product computations such as counting matchings. It is inspired by holographic algorithms and is equivalent to tensor networks, with counting CSP being a special case. A classification for Holant…
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…
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…
We prove a complexity dichotomy theorem for Holant Problems on 3-regular graphs with an arbitrary complex-valued edge function. Three new techniques are introduced: (1) higher dimensional iterations in interpolation; (2) Eigenvalue Shifted…
Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…
Holant problems are a family of counting problems on graphs, parametrised by sets of complex-valued functions of Boolean inputs. Holant^c denotes a subfamily of those problems, where any function set considered must contain the two unary…
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…
Holant problems are a general framework to study the algorithmic complexity of counting problems. Both counting constraint satisfaction problems and graph homomorphisms are special cases. All previous results of Holant problems are over the…
Recent progress in studies of holographic dualities, originally motivated by insights from string theory, has led to a confluence with concepts and techniques from quantum information theory. A particularly successful approach has involved…
We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…
Holant problem is a general framework to study the computational complexity of counting problems. We prove a complexity dichotomy theorem for Holant problems over Boolean domain with non-negative weights. It is the first complete Holant…
This paper presents Holbert: a work-in-progress pedagogical proof assistant and online textbook platform, aimed at the educational use-case, specifically for the teaching of programming language theory. Holbert allows proof exercises and…
We review the developments in the past decade on holographic entanglement entropy, a subject that has garnered much attention owing to its potential to teach us about the emergence of spacetime in holography. We provide an introduction to…
Holography is a vital tool used in various applications from microscopy, solar energy, imaging, display to information encryption. Generation of a holographic image and reconstruction of object/hologram information from a holographic image…