Related papers: A Behavioural Theory of Recursive Algorithms
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…
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…
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…
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…
We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family…
The behavioural theory of concurrent systems states that any concurrent system can be captured by a behaviourally equivalent concurrent Abstract State Machine (cASM). While the theory in general assumes shared locations, it remains valid,…
We develop a correspondence between the theory of sequential algorithms and classical reasoning, via Kreisel's no-counterexample interpretation. Our framework views realizers of the no-counterexample interpretation as dynamic processes…
To reversify an arbitrary sequential algorithm $A$, we gently instrument $A$ with bookkeeping machinery. The result is a step-for-step reversible algorithm that mimics $A$ step-for-step and stops exactly when $A$ does. Without loss of…
Most ideas about what an algorithm is are very similar. Basic operations are used for transforming objects. The evaluation of internal and external states by relations has impact on the further process. A more precise definition can lead to…
Recursive Neural Networks are non-linear adaptive models that are able to learn deep structured information. However, these models have not yet been broadly accepted. This fact is mainly due to its inherent complexity. In particular, not…
Although algorithm is one of the central subjects, there have been little common understandings of what an algorithm is. For example, Gurevich view algorithms as abstract state machines, while others view algorithms as recursors. We promote…
It is well-known that Abstract State Machines (ASMs) can simulate "step-by-step" any type of machines (Turing machines, RAMs, etc.). We aim to overcome two facts: 1) simulation is not identification, 2) the ASMs simulating machines of some…
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…
Over the past two decades, Yuri Gurevich and his colleagues have formulated axiomatic foundations for the notion of algorithm, be it classical, interactive, or parallel, and formalized them in the new generic framework of abstract state…
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 decentralized stochastic control (or stochastic team theory) and game theory, if there is a pre-defined order in a system in which agents act, the system is called \textit{sequential}, otherwise it is non-sequential. Much of the…
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…
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…
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…
How should future neural reasoning systems implement extended computation? Recursive Reasoning Models (RRMs) offer a promising alternative to autoregressive sequence extension by performing iterative latent-state refinement with shared…