Related papers: Modeling Asymptotic Complexity Using ACL2
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
The concept of linearity plays a central role in both mathematics and computer science, with distinct yet complementary meanings. In mathematics, linearity underpins functions and vector spaces, forming the foundation of linear algebra and…
Formal software verification techniques are widely used to specify and prove the functional correctness of programs. However, nonfunctional properties such as time complexity are usually carried out with pen and paper. Inefficient code in…
Continuous cellular automata (CCAs) have evolved from discrete lookup tables to continuous partial differential equation (PDE) formulations in the search for novel forms of complexity. Despite innovations in qualitative behavior, analytical…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…
The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (7). There is a large variety of such symbolic sequences, ranging from texts written in natural languages,…
In estimating the complexity of objects, in particular of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these…
Effective complexity measures the information content of the regularities of an object. It has been introduced by M. Gell-Mann and S. Lloyd to avoid some of the disadvantages of Kolmogorov complexity, also known as algorithmic information…
Verification of algorithms and data structures utilized in modern autonomous and semi-autonomous vehicles for land, sea, air, and space presents a significant challenge. Autonomy algorithms, e.g., route planning, pattern matching, and…
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms…
The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. The regularities are modeled by means of ensembles, that is probability distributions on…
SOFT ('Second-Order Functions and Theorems') is a tool to mimic second-order functions and theorems in the first-order logic of ACL2. Second-order functions are mimicked by first-order functions that reference explicitly designated…
The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear…
Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical…
We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by…
We survey results about computational complexity of the word problem in groups, Dehn functions of groups and related problems.
Using an interactive theorem prover to reason about programs involves a sequence of interactions where the user challenges the theorem prover with conjectures. Invariably, many of the conjectures posed are in fact false, and users often…