Related papers: An insertion algorithm for catabolizability
We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…
Although neural networks can solve very complex machine-learning problems, the theoretical reason for their generalizability is still not fully understood. Here we use Wang-Landau Mote Carlo algorithm to calculate the entropy (logarithm of…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
The semina\"ive algorithm can materialise all consequences of arbitrary datalog rules, and it also forms the basis for incremental algorithms that update a materialisation as the input facts change. Certain (combinations of) rules, however,…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
We discuss some applications of fusion rules and intertwining operators in the representation theory of cyclic orbifolds of the triplet vertex operator algebra. We prove that the classification of irreducible modules for the orbifold vertex…
We propose an iterative algorithm to investigate the cooperative evolution dominated by information encoded within state spaces in a random quantum cellular automaton. Inspired by the 2-gram model in statistical linguistics, the updates of…
In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the…
The Tutte polynomial is the most general invariant of matroids and graphs that can be computed recursively by deleting and contracting edges. We generalize this invariant to any class of combinatorial objects with deletion and contraction…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
We introduce an efficient way, called Newton algorithm, to study arbitrary ideals in C[[x,y]], using a finite succession of Newton polygons. We codify most of the data of the algorithm in a useful combinatorial object, the Newton tree. For…
Algorithms for computing congruence closure of ground equations over uninterpreted symbols and interpreted symbols satisfying associativity and commutativity (AC) properties are proposed. The algorithms are based on a framework for…
Using an appropriate notion of locally convex Kasparov modules, we show how to induce isomorphisms under a large class of functors on the category of locally convex algebras; examples are obtained from spectral triples. Our considerations…
Word embedding techniques heavily rely on the abundance of training data for individual words. Given the Zipfian distribution of words in natural language texts, a large number of words do not usually appear frequently or at all in the…
If a set $\mathbb{G}$ of quantum gates is countable, then the operators that can be exactly represented by a circuit over $\mathbb{G}$ form a strict subset of the collection of all unitary operators. When $\mathbb{G}$ is universal, one…
The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…
We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of $n$ items, each associated with a non-negative weight, and $T$ time…
Combining the representations of the words that make up a sentence into a cohesive whole is difficult, since it needs to account for the order of words, and to establish how the words present relate to each other. The solution we propose…
For a countable amenable group \Gamma and an element f in the integral group ring Z\Gamma being invertible in the group von Neumann algebra of \Gamma, we show that the entropy of the shift action of \Gamma on the Pontryagin dual of the…