Related papers: Modeling Asymptotic Complexity Using ACL2

When verifying computer systems we sometimes want to study their asymptotic behaviors, i.e., how they behave in the long run. In such cases, we need real analysis, the area of mathematics that deals with limits and the foundations of…

ACL2 provides a systems programming capability that allows one to write code that uses and extends ACL2 inside of ACL2. However, for soundness reasons, ACL2 bars the unrestricted use of certain kinds of programming constructs, like…

We present a framework in Isabelle for verifying asymptotic time complexity of imperative programs. We build upon an extension of Imperative HOL and its separation logic to include running time. In addition to the basic arguments, our…

A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis…

Iterative algorithms are traditionally expressed in ACL2 using recursion. On the other hand, Common Lisp provides a construct, loop, which -- like most programming languages -- provides direct support for iteration. We describe an ACL2…

We present a method for synthesizing recursive functions that satisfy both a functional specification and an asymptotic resource bound. Prior methods for synthesis with a resource metric require the user to specify a concrete expression…

Computational models of human language often involve combinatorial problems. For instance, a probabilistic parser may marginalize over exponentially many trees to make predictions. Algorithms for such problems often employ dynamic…

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…

This paper takes an empirical look at asymptotic runtime growth rates for the most widely used algorithms for solving linear programming (LP) problems across a set of six optimization application areas that are known to produce large and…

ACL2 was used to prove properties of two simplification procedures. The procedures differ in complexity but solve the same programming problem that arises in the context of a resolution/paramodulation theorem proving system. Term rewriting…

We present a polynomial-time algorithm that obtains a set of Asymptotic Linear Programs (ALPs) from a given linear system S, such that one of these ALPs admits a feasible solution if and only if S admits a feasible solution. We also show…

Asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity of a class of dynamic programming algorithms including matrix chain multiplication, optimal polygon triangulation, and the construction of optimal binary…

In this paper, we analyze the complexity of functional programs written in the interaction-net computation model, an asynchronous, parallel and confluent model that generalizes linear-logic proof nets. Employing user-defined sized and…

We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…

Behavioral synthesis involves compiling an Electronic System-Level (ESL) design into its Register-Transfer Level (RTL) implementation. Loop pipelining is one of the most critical and complex transformations employed in behavioral synthesis.…

In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…

The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that…

Given a reference computer, Kolmogorov complexity is a well defined function on all binary strings. In the standard approach, however, only the asymptotic properties of such functions are considered because they do not depend on the…

We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of…

This paper deals with the problem of the requirements for quantum systems that enable one to design efficient quantum algorithms. We rise the issue of the possibility to utilise the non-complete networks for algorithmic purposes. In…