Related papers: On the Complexity of Determinations
Decision-making problems in uncertain or stochastic domains are often formulated as Markov decision processes (MDPs). Policy iteration (PI) is a popular algorithm for searching over policy-space, the size of which is exponential in the…
A standard informal method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input, and then to compute a closed-form upper bound on that recurrence. We give…
The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use function is explicitly specified. This elaboration…
Computational models typically assume that operations are applied in a fixed sequential order. In recent years several works have looked at relaxing this assumption, considering computations without any fixed causal structure and showing…
Enclosing depth is a recently introduced depth measure which gives a lower bound to many depth measures studied in the literature. So far, enclosing depth has only been studied from a combinatorial perspective. In this work, we give the…
A central method for analyzing the asymptotic complexity of a functional program is to extract and then solve a recurrence that expresses evaluation cost in terms of input size. The relevant notion of input size is often specific to a…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
Quantum Parametric Circuits are constructed as an alternative to reduce the size of quantum circuits, meaning to decrease the number of quantum gates and, consequently, the depth of these circuits. However, determining the optimal circuit…
This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
This dissertation proves lower bounds on the inherent difficulty of deciding flow analysis problems in higher-order programming languages. We give exact characterizations of the computational complexity of 0CFA, the $k$CFA hierarchy, and…
We study a simple model for the evolution of the cost (or more generally the performance) of a technology or production process. The technology can be decomposed into $n$ components, each of which interacts with a cluster of $d-1$ other,…
The logical depth with significance $b$ of a finite binary string $x$ is the shortest running time of a binary program for $x$ that can be compressed by at most $b$ bits. There is another definition of logical depth. We give two theorems…
As fragments of first-order logic, Description logics (DLs) do not provide nonmonotonic features such as defeasible inheritance and default rules. Since many applications would benefit from the availability of such features, several…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…
In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…
In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a…
Standard Transformers have a fixed computational depth, fundamentally limiting their ability to generalize to tasks requiring variable-depth reasoning, such as multi-hop graph traversal or nested logic. We propose a depth-recurrent…
We begin development of a method for studying dynamical systems using concepts from computational complexity theory. We associate families of decision problems, called telic problems, to dynamical systems of a certain class. These decision…
The Weihrauch degrees are a tool to gauge the computational difficulty of mathematical problems. Often, what makes these problems hard is their discontinuity. We look at discontinuity in its purest form, that is, at otherwise constant…