Related papers: An Overview Of Some Semantic And Syntactic Complex…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the…
Measuring text complexity is an essential task in several fields and applications (such as NLP, semantic web, smart education, etc.). The semantic layer of text is more tacit than its syntactic structure and, as a result, calculation of…
In this paper, we introduce relative LS category of a map and study some of its properties. Then we introduce `higher topological complexity' of a map, a homotopy invariant. We give a cohomological lower bound and compare it with previously…
Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…
Predicting the structure of a discourse is challenging because relations between discourse segments are often implicit and thus hard to distinguish computationally. I extend previous work to classify implicit discourse relations by…
The point of this note is to prove that a language is in the complexity class PP if and only if the strings of the language encode valid inferences in a Bayesian network defined using function-free first-order logic with equality.
We investigate enumerability properties for classes of sets which permit recursive, lexicographically increasing approximations, or left-r.e. sets. In addition to pinpointing the complexity of left-r.e. Martin-L\"{o}f, computably, Schnorr,…
There is no single definition of complexity (Edmonds 1999; Gershenson 2008; Mitchell 2009; De Domenico, et al., 2019), as it acquires different meanings in different contexts. A general notion is the amount of information required to…
We define and study a new notion of "robust simulations" between complexity classes which is intermediate between the traditional notions of infinitely-often and almost-everywhere, as well as a corresponding notion of "significant…
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
The relationship between the complexity classes $P$ and $NP$ is an unsolved question in the field of theoretical computer science. In the first part of this paper, a lattice framework is proposed to handle the 3-CNF-SAT problems, known to…
The study of complexity and optimization in decision theory involves both partial and complete characterizations of preferences over decision spaces in terms of real-valued monotones. With this motivation, and following the recent…
This paper establishes the separation of complexity classes $\mathbf{P}$ and $\mathbf{NP}$ through a novel homological algebraic approach grounded in category theory. We construct the computational category $\mathbf{Comp}$, embedding…
This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies.…
We initiate the study of the complexity-theoretic properties of convex logics in team semantics. We focus on the extension of classical propositional logic with the nonemptiness atom NE, a logic known to be both convex and union closed. We…
New classes of distance-constrained structures are introduced, namely string-node nets and meshes, a mesh being a string-node net for which the nodes are dense in the strings. Various construction schemes are given including the minimal…
The state complexity, respectively, nondeterministic state complexity of a regular language $L$ is the number of states of the minimal deterministic, respectively, of a minimal nondeterministic finite automaton for $L$. Some of the most…
For several classical nonnegative integer functions, we investigate if they are members of the counting complexity class #P or not. We prove #P membership in surprising cases, and in other cases we prove non-membership, relying on standard…
Infinite sequences are of tremendous theoretical and practical importance, and in the Information Age sequences of 0s and 1s are of particular interest. Over the past century, the field of symbolic dynamics has developed to study sequences…