Related papers: Completeness in Polylogarithmic Time and Space
We consider the long-standing question of whether every regular LB-space is complete. This problem has been open since the 1950s and originates in Grothendieck's early work in functional analysis. Rather than seeking a direct proof or…
Computational complexity characterizes the usage of spatial and temporal resources by computational processes. In the classical theory of computation, e.g. in the Turing Machine model, computational processes employ only local space and…
We clarify and discuss a misunderstanding between uniform completeness and metric completeness, that has appeared in the literature in a study on the Alexandrov topology for a spacetime.
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
Depth of an object concerns a tradeoff between computation time and excess of program length over the shortest program length required to obtain the object. It gives an unconditional lower bound on the computation time from a given program…
Standpoint linear temporal logic SLTL is a recent formalism able to model possibly conflicting commitments made by distinct agents, taking into account aspects of temporal reasoning. In this paper, we analyse the computational properties of…
Typestate systems ensure many desirable properties of imperative programs, including initialization of object fields and correct use of stateful library interfaces. Abstract sets with cardinality constraints naturally generalize typestate…
Valiant introduced matchgate computation and holographic algorithms. A number of seemingly exponential time problems can be solved by this novel algorithmic paradigm in polynomial time. We show that, in a very strong sense, matchgate…
This chapter serves as an introduction to systems engineering focused on the broad issues surrounding realizing complex integrated systems. What is a system? We pose a number of possible definitions and perspectives, but leave open the…
Promise CSPs are a relaxation of constraint satisfaction problems where the goal is to find an assignment satisfying a relaxed version of the constraints. Several well-known problems can be cast as promise CSPs including approximate graph…
The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of…
We explore the consequences of requiring that quantum theories of gravity be unitary, mostly focusing on simple cosmological models to illustrate the main points. We show that unitarity for a clock that encounters a classical singularity at…
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…
Most work on computational complexity is concerned with time. However this course will try to show that program-size complexity, which measures algorithmic information, is of much greater philosophical significance. I'll discuss how one can…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…
We show that under mild assumptions for a problem whose solutions admit a dynamic programming-like recurrence relation, we can still find a solution under additional packing constraints, which need to be satisfied approximately. The number…
We introduce a concept of efficiency for which we can prove that it applies to all paddable languages, but still does not conflict with potential worst case intractability. Note that the family of paddable languages apparently includes all…
One of the central open problems to classify the computational complexity of finite-domain constraint satisfaction problems within P is to prove better algorithmic results for CSPs with a Maltsev polymorphism; we do not even know whether…