Related papers: Behavioural Theory of Reflective Algorithms I: Ref…
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…
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…
"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…
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…
Test-time scaling methods improve the capabilities of large language models (LLMs) by increasing the amount of compute used during inference to make a prediction. Inference-time compute can be scaled in parallel by choosing among multiple…
The Rational Speech Acts (RSA) model treats language use as a recursive process in which probabilistic speaker and listener agents reason about each other's intentions to enrich the literal semantics of their language along broadly Gricean…
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,…
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…
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…
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…
Recursive reasoning models such as Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM) show that small, weight-shared networks can solve compute-heavy and NP puzzles by iteratively refining latent states, but their training…
Representational Similarity Analysis (RSA) is a technique developed by neuroscientists for comparing activity patterns of different measurement modalities (e.g., fMRI, electrophysiology, behavior). As a framework, RSA has several advantages…
Sequential Recommender Systems (SRSs) have emerged as a highly efficient approach to recommendation systems. By leveraging sequential data, SRSs can identify temporal patterns in user behaviour, significantly improving recommendation…
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…
This paper presents an algebraic theory of instruction sequences with instructions for a random access machine (RAM) as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction…
We present a theoretical study of continual and experiential learning in large language model agents that combine episodic memory with reinforcement learning. We argue that the key mechanism for continual adaptation, without updating model…
Cooperative behavior is prevalent in both human society and nature. Understanding the emergence and maintenance of cooperation among self-interested individuals remains a significant challenge in evolutionary biology and social sciences.…
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…
What computational principles underlie human pragmatic reasoning? A prominent approach to pragmatics is the Rational Speech Act (RSA) framework, which formulates pragmatic reasoning as probabilistic speakers and listeners recursively…
Reaction automata are a formal model that has been introduced to investigate the computing powers of interactive behaviors of biochemical reactions([14]). Reaction automata are language acceptors with multiset rewriting mechanism whose…