Related papers: Sophistication vs Logical Depth
We comment on a recent paper by D'Abramo [Chaos, Solitons & Fractals, 25 (2005) 29], focusing on the author's statement that an algorithm can produce a list of strings containing at least one string whose algorithmic complexity is greater…
In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides…
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…
Being able to objectively characterise the intrinsic complexity of behavioural patterns resulting from human or animal decisions is fundamental for deconvolving cognition and designing autonomous artificial intelligence systems. Yet…
Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of…
The logical connectives typically found in programming languages are similar to their mathematical counterparts, yet different due to their short-circuit behaviour -- when evaluating them, the second argument is only evaluated if the first…
Structured reasoning over natural language inputs remains a core challenge in artificial intelligence, as it requires bridging the gap between unstructured linguistic expressions and formal logical representations. In this paper, we propose…
In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…
Software implements a significant proportion of functionality in factory automation. Thus, efficient development and the reuse of software parts, so-called units, enhance competitiveness. Thereby, complex control software units are more…
Written language is complex. A written text can be considered an attempt to convey a meaningful message which ends up being constrained by language rules, context dependence and highly redundant in its use of resources. Despite all these…
Beam search and exhaustive search are two extreme ends of text decoding algorithms with respect to the search depth. Beam search is limited in both search width and depth, whereas exhaustive search is a global search that has no such…
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…
This paper uses the concept of algorithmic efficiency to present a unified theory of intelligence. Intelligence is defined informally, formally, and computationally. We introduce the concept of Dimensional complexity in algorithmic…
A property, or statistical functional, is said to be elicitable if it minimizes expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and…
There is a growing interest in techniques for detecting whether a logic specification is satisfied too easily, or vacuously. For example, the specification "every request is eventually followed by an acknowledgment" is satisfied vacuously…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…
Good software has high cohesion and low coupling is clumsy, obscure, and in some certain cases could be actually a harmful state of being. It is clumsy because there is no perfect correlation between higher cohesiveness and optimum design,…
Simplicity is held by many to be the key to general intelligence. Simpler models tend to "generalise", identifying the cause or generator of data with greater sample efficiency. The implications of the correlation between simplicity and…
In data languages the positions of strings and trees carry a label from a finite alphabet and a data value from an infinite alphabet. Extensions of automata and logics over finite alphabets have been defined to recognize data languages,…