Related papers: A new Holant dichotomy inspired by quantum computa…

Causal modelling frameworks link observable correlations to causal explanations, which is a crucial aspect of science. These models represent causal relationships through directed graphs, with vertices and edges denoting systems and…

We investigate the Constraint Satisfaction Problem (CSP) over templates with a group structure, and algorithms solving CSP that are equivariant, i.e. invariant under a natural group action induced by a template. Our main result is a method…

In the constraint satisfaction problem ($CSP$), the aim is to find an assignment of values to a set of variables subject to specified constraints. In the minimum cost homomorphism problem ($MinHom$), one is additionally given weights…

If two parties share sufficient entanglement, they are able to implement any channel on a shared bipartite state via non-local quantum computation -- a protocol consisting of local operations and a single simultaneous round of quantum…

We present a new method for inferring complexity properties for a class of programs in the form of flowcharts annotated with loop information. Specifically, our method can (soundly and completely) decide if computed values are polynomially…

Holographic duality describes gravitational theories in terms of quantum many-body systems. In holography, quantum information theory provides a crucial tool that directly connects microscopic structures of these systems to the geometries…

For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…

Counting the number of homomorphisms of a pattern graph H in a large input graph G is a fundamental problem in computer science. There are myriad applications of this problem in databases, graph algorithms, and network science. Often, we…

We study the problem of query evaluation on probabilistic graphs, namely, tuple-independent probabilistic databases over signatures of arity two. We focus on the class of queries closed under homomorphisms, or, equivalently, the infinite…

A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a…

This is the fourth paper in the CayleyPy project, which applies AI methods to the exploration of large graphs. In this work, we suggest the existence of a new discrete version of holographic string dualities for this setup, and discuss…

In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

We discover new P-time computable six-vertex models on planar graphs beyond Kasteleyn's algorithm for counting planar perfect matchings. We further prove that there are no more: Together, they exhaust all P-time computable six-vertex models…

We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and…

Hamiltonian encoding is a methodology for revealing the mechanism behind the dynamics governing controlled quantum systems. In this paper, following Mitra and Rabitz [Phys. Rev. A 67, 033407 (2003)], we define mechanism via pathways of…

We develop an algebraic and operational framework for quantum isomorphisms of hypergraphs, using tools from compact quantum group theory. We introduce a new synchronous version of the hypergraph isomorphism game whose game algebra uniformly…

Lattice-based cryptography is not only for thwarting future quantum computers, and is also the basis of Fully Homomorphic Encryption. Motivated from the advantage of graph homomorphisms we combine graph homomorphisms with graph total…

Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between…

In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…