Related papers: Sophistication vs Logical Depth
Cognitive complexity measures quantify human difficulty in understanding the source code based on cognitive informatics foundation. The discipline derives cognitive complexity on a basis of fundamental software factors i.e, inputs, outputs,…
Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…
The term {\em complexity} is used informally both as a quality and as a quantity. As a quality, complexity has something to do with our ability to understand a system or object -- we understand simple systems, but not complex ones. On…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
Systems for language understanding have become remarkably strong at overcoming linguistic imperfections in tasks involving phrase matching or simple reasoning. Yet, their accuracy drops dramatically as the number of reasoning steps…
Many philosophers of physics maintain that a physical theory that exhibits (certain kinds of) symmetries is flawed, on the grounds that such theories posit "excess structure". In an influential paper, Dewar [2019, "Sophistication about…
A suffix tree is a data structure used mainly for pattern matching. It is known that the space complexity of simple suffix trees is quadratic in the length of the string. By a slight modification of the simple suffix trees one gets the…
Large language models (LLMs) often benefit from verbalized reasoning at inference time, but it remains unclear which aspects of task difficulty these extra reasoning tokens address. To investigate this question, we formalize a framework…
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 fine approach to measure information dependence is based on the total conditional complexity CT(y|x), which is defined as the minimal length of a total program that outputs y on the input x. It is known that the total conditional…
We introduce derivation depth-a computable metric of the reasoning effort needed to answer a query based on a given set of premises. We model information as a two-layered structure linking abstract knowledge with physical carriers, and…
In this manuscript, we derive the principle of conservation of computational complexity. We measure computational complexity as the number of binary computations (decisions) required to solve a problem. Every problem then defines a unique…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
Satisfiability solvers are increasingly playing a key role in software verification, with particularly effective use in the analysis of security vulnerabilities. String processing is a key part of many software applications, such as…
The possibility of translating logic programs into functional ones has long been a subject of investigation. Common to the many approaches is that the original logic program, in order to be translated, needs to be well-moded and this has…
We develop a static complexity analysis for a higher-order functional language with structural list recursion. The complexity of an expression is a pair consisting of a cost and a potential. The former is defined to be the size of the…
Large language models demonstrate limited capability in proficiency-controlled sentence simplification, particularly when simplifying across large readability levels. We propose a framework that decomposes complex simplifications into…
Recent theoretical results show transformers cannot express sequential reasoning problems over long inputs, intuitively because their computational depth is bounded. However, prior work treats the depth as a constant, leaving it unclear to…
We consider the task of performing probabilistic inference with probabilistic logical models. Many algorithms for approximate inference with such models are based on sampling. From a logic programming perspective, sampling boils down to…