相关论文: Interactive Small-Step Algorithms II: Abstract Sta…

In earlier work, the Abstract State Machine Thesis -- that arbitrary algorithms are behaviorally equivalent to abstract state machines -- was established for several classes of algorithms, including ordinary, interactive, small-step…

Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm…

We develop a behavioural theory of reflective parallel algorithms (RAs), i.e. synchronous parallel algorithms that can modify their own behaviour. The theory comprises a set of postulates defining the class of RAs, an abstract machine…

This dialog paper offers a preview and provides a foretaste of an upcoming work on the axiomatization of basic interactive algorithms. The modern notion of algorithm was elucidated in the 1930s--1950s. It was axiomatized a quarter of a…

We propose a formalization of generic algorithms that includes analog algorithms. This is achieved by reformulating and extending the framework of abstract state machines to include continuous-time models of computation. We prove that every…

The technique of abstracting abstract machines (AAM) provides a systematic approach for deriving computable approximations of evaluators that are easily proved sound. This article contributes a complementary step-by-step process for…

The behavior and architecture of large scale discrete state systems found in computer software and hardware can be specified and analyzed using a particular class of primitive recursive functions. This paper begins with an illustration of…

A behavioural theory consists of machine-independent postulates characterizing a particular class of algorithms or systems, an abstract machine model that provably satisfies these postulates, and a rigorous proof that any algorithm or…

The majorization theory has been applied to analyze the mathematical structure of quantum algorithms. An empirical conclusion by numerical simulations obtained in the previous literature indicates that step-by-step majorization seems to…

"What is an algorithm?" is a fundamental question of computer science. Gurevich's behavioural theory of sequential algorithms (aka the sequential ASM thesis) gives a partial answer by defining (non-deterministic) sequential algorithms…

We develop a logic which enables reasoning about single steps of non-deterministic parallel Abstract State Machines (ASMs). Our logic builds upon the unifying logic introduced by Nanchen and St\"ark for reasoning about hierarchical…

In this note, we defend that the notion of algorithm as a set of execution traces is somewhat independent of the notion of abstract state machine. It can be reformulated in the more general framework of small step operational semantics.

We develop a behavioural theory of reflective sequential algorithms (RSAs), i.e. sequential algorithms that can modify their own behaviour. The theory comprises a set of language-independent postulates defining the class of RSAs, an…

We study normalisation of multistep strategies, strategies that reduce a set of redexes at a time, focussing on the notion of necessary sets, those which contain at least one redex that cannot be avoided in order to reach a normal form.…

This paper introduces a new algorithm for the induction if complex finite state automata from samples of behavior. The algorithm is based on information theoretic principles. The algorithm reduces the search space by many orders of…

In article "Sequential abstract state machines capture sequential algorithms", one of us axiomatized sequential algorithms by means of three postulates: sequential time, abstract state, and bounded exploration postulates. Here we give a…

This work introduces a new abstraction technique for reducing the state space of large, discrete-time labelled Markov chains. The abstraction leverages the semantics of interval Markov decision processes and the existing notion of…

This paper describes a first step towards the definition of an abstract machine for linguistic formalisms that are based on typed feature structures, such as HPSG. The core design of the abstract machine is given in detail, including the…

Starting from Gurevich's thesis for sequential algorithms (the so-called "sequential ASM thesis"), we propose a characterization of the behaviour of sequential algorithms enriched with reflection. That is, we present a set of postulates…

Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…