Related papers: The Cook-Reckhow definition
Below is a translation from my Russian paper. I added references, unavailable to me in Moscow. Similar results have been also given in [Schnorr Stumpf 75] (see also [Lynch 75]). Earlier relevant work (classical theorems like Compression,…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
It is not known what the limitations are on using quantum computation to speed up classical computation. An example would be the power to speed up PSPACE-complete computations. It is also not known what the limitations are on the duration…
We establish various complexity results for the entailment problem between formulas in Separation Logic with user-defined predicates denoting recursive data structures. The considered fragments are characterized by syntactic conditions on…
The term complexity derives etymologically from the Latin plexus, which means interwoven. Intuitively, this implies that something complex is composed by elements that are difficult to separate. This difficulty arises from the relevant…
The reflection principle is the statement that if a sentence is provable then it is true. Reflection principles have been studied for first-order theories, but they also play an important role in propositional proof complexity. In this…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as $\SigmaPtwo$-complete, and the complexity of the credulous and skeptical…
Most state-of-the-art satisfiability algorithms today are variants of the DPLL procedure augmented with clause learning. The main bottleneck for such algorithms, other than the obvious one of time, is the amount of memory used. In the field…
For a linear code, deep holes are defined to be vectors that are further away from codewords than all other vectors. The problem of deciding whether a received word is a deep hole for generalized Reed-Solomon codes is proved to be…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
Autoepistemic logic extends propositional logic by the modal operator L. A formula that is preceded by an L is said to be "believed". The logic was introduced by Moore 1985 for modeling an ideally rational agent's behavior and reasoning…
A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees,…
This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex…
The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…
Satisfiability problems play a central role in computer science and engineering as a general framework for studying the complexity of various problems. Schaefer proved in 1978 that truth satisfaction of propositional formulas given a…
Proof formats for SAT solvers have diversified over the last decade, enabling new features such as extended resolution-like capabilities, very general extension-free rules, inclusion of proof hints, and pseudo-boolean reasoning.…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
Dickson's Lemma is a simple yet powerful tool widely used in termination proofs, especially when dealing with counters or related data structures. However, most computer scientists do not know how to derive complexity upper bounds from such…