Mechanical verification of mutually recursive procedures

Many sequences from number theory, such as the primes, are defined by recursive procedures, often leading to complex local behavior, but also to graphical similarity on different scales — a property that can be analyzed by fractal dimension. This paper computes sample fractal dimensions from the graphs of some number-theoretic functions. It argues for the usefulness of empirical fractal dimension as a distinguishing characteristic of the graph. Also, it notes a remarkable similarity between two apparently unrelated sequences: the persistence of a number, and the memory of a prime. This similarity is quantified using fractal dimension.

Download Full-text

Real-Time Properties of Indirect Recursive Procedures

Information and Computation ◽

10.1006/inco.2001.3042 ◽

2001 ◽

Vol 171 (2) ◽

pp. 156-182 ◽

Cited By ~ 2

Author(s):

Johann Blieberger

Keyword(s):

Real Time ◽

Recursive Procedures

Download Full-text

Mechanical Verification of Transactional Memories with Non-transactional Memory Accesses

Computer Aided Verification - Lecture Notes in Computer Science ◽

10.1007/978-3-540-70545-1_13 ◽

2008 ◽

pp. 121-134 ◽

Cited By ~ 15

Author(s):

Ariel Cohen ◽

Amir Pnueli ◽

Lenore D. Zuck

Keyword(s):

Transactional Memory ◽

Mechanical Verification ◽

Memory Accesses ◽

Transactional Memories

Download Full-text

Proving total correctness of recursive procedures

Information and Computation ◽

10.1016/0890-5401(90)90037-i ◽

1990 ◽

Vol 84 (2) ◽

pp. 129-162 ◽

Cited By ~ 13

Author(s):

Pierre America ◽

Frank de Boer

Keyword(s):

Total Correctness ◽

Recursive Procedures

Download Full-text

Mechanical verification of transaction processing systems

ICFEM 2000. Third IEEE International Conference on Formal Engineering Methods ◽

10.1109/icfem.2000.873809 ◽

2002 ◽

Cited By ~ 2

Author(s):

D. Chkliaev ◽

J. Hooman ◽

P. van der Stok

Keyword(s):

Transaction Processing ◽

Mechanical Verification ◽

Transaction Processing Systems

Download Full-text

Statistical Mechanical Verification of the Gibbs Adsorption Equation

SOLID SURFACES - Advances in Chemistry ◽

10.1021/ba-1961-0033.ch036 ◽

1961 ◽

pp. 340-347 ◽

Cited By ~ 2

Author(s):

FRANK P. BUFF

Keyword(s):

Mechanical Verification ◽

Adsorption Equation ◽

Gibbs Adsorption Equation ◽

Statistical Mechanical

Download Full-text

Proof rules for recursive procedures

Formal Aspects of Computing ◽

10.1007/bf01211249 ◽

1993 ◽

Vol 5 (6) ◽

pp. 554-570 ◽

Cited By ~ 12

Author(s):

Wim H. Hesselink

Keyword(s):

Proof Rules ◽

Recursive Procedures

Download Full-text

Towards an Integrative Model of Deductive-Inductive Commonsense Reasoning

Machine Learning Methods for Commonsense Reasoning Processes ◽

10.4018/978-1-60566-810-9.ch009 ◽

2010 ◽

pp. 245-278

Author(s):

Xenia Naidenova

Keyword(s):

Incremental Algorithm ◽

Integrative Model ◽

Commonsense Reasoning ◽

Recursive Procedures ◽

Good Classification ◽

Mental Acts ◽

Made In

The most important steps in the direction to an integrative model of deductive-inductive commonsense reasoning are made in this chapter. The decomposition of inferring good classification tests is advanced into two kinds of subtasks that are in accordance with human mental acts. This decomposition allows modeling incremental inductive-deductive inferences. We give two basic recursive procedures based on two kinds of subtasks for inferring all good maximally redundant classification tests (GMRTs): ASTRA and DIAGaRa. An incremental algorithm INGOMAR for inferring all GMRTs is presented too. The problems of creating an integrative inductive-deductive model of commonsense reasoning are discussed in the last section of this chapter.

Download Full-text