arXiv subjects

Anton Salikhmetov

Publications and source records attributed to Anton Salikhmetov.

16 recordsLinked to original sources

arXiv2018

Elementary Microeconomics of the Talmudic Rule

This paper takes a look at the Talmudic rule aka the 1/N rule aka the uniform investment strategy from the viewpoint of elementary microeconomics. Specifically, we derive the cardinal utility function for a Talmud-obeying agent which happens to have the Cobb-Douglas form. Further, we investigate individual supply and demand due to rebalancing and compare them to market depth of an exchange. Finally, we discuss how operating as a liquidity provider can benefit the Talmud-obeying agent with every exchange transaction in terms of the identified utility function.

q-fin.GN↗

arXiv2018

Upward confluence in the interaction calculus

The lambda calculus is not upward confluent, one of counterexamples known thanks to Plotkin. This paper investigates upward confluence in the interaction calculus. Can an interaction system have this property? We positively answer this question and also provide a necessary and sufficient condition for stronger one-step upward confluence which happens to be very restrictive. However, the provided condition is not necessary for upward confluence as we prove that the interaction system of the linear lambda calculus is upward confluent.

cs.LO↗

arXiv2018

Lambda Calculus with Explicit Read-back

This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its properties. Namely, we verify that it correctly represents the lambda calculus. Further, we show that there is exactly one reduction sequence that starts with any term in our term rewriting system. Finally, we represent the leftmost strategy which is known to be normalizing.

cs.LO↗

arXiv2018

An impure solution to the problem of matching fans

We propose an algorithm to solve the problem of matching fans in interaction net implementations of optimal reduction for the pure untyped lambda calculus without use of any additional agent types. The algorithm relies upon a specific interaction nets reduction strategy and involves side effects in one of interaction rules.

cs.LO↗

arXiv2017

Parallel needed reduction for pure interaction nets

Reducing interaction nets without any specific strategy benefits from constant time per step. On the other hand, a canonical reduction step for weak reduction to interface normal form is linear by depth of terms. In this paper, we refine the weak interaction calculus to reveal the actual cost of its reduction. As a result, we obtain a notion of needed reduction that can be implemented in constant time per step without allowing any free ports and without sacrificing parallelism.

cs.LO↗

arXiv2017

A better model of computation for digital physics?

This note is meant to invite the reader to consider interaction nets, a relatively recently discovered model of computation, as a possible alternative for cellular automata which are often employed as the basis for digital physics. Defined as graph-like structures (in contrast to the grids for cellular automata), interaction nets possess a set of interesting properties, such as locality, linearity, and strong confluence, which together result in so-called clockless computation in the sense that they do not require any global clock in order to operate. We believe that an attempt of using interaction nets as a replacement for cellular automata may lead to a new view in digital physics.

cs.LO↗

arXiv2017

Optimal Reduction without Oracle?

We suggest an approach to solve the problem of matching fans in interaction net implementations of optimal reduction for the pure untyped lambda calculus without use of any additional agent types. Our implementation supports a wider class of lambda terms than the abstract version of Lamping's algorithm and beats the interaction net implementation of closed reduction by the total number of interactions.

cs.LO↗

arXiv2016

Token-passing Optimal Reduction with Embedded Read-back

We introduce a new interaction net implementation of optimal reduction for the pure untyped lambda calculus. Unlike others, our implementation allows to reach normal form regardless of the interaction net reduction strategy using the approach of so-called token-passing nets and a non-deterministic extension for interaction nets. Another new feature is the read-back mechanism implemented without leaving the formalism of interaction nets.

cs.LO↗

arXiv2015

A token-passing net implementation of optimal reduction with embedded read-back

In this paper, we introduce a new interaction net implementation of optimal reduction for pure untyped lambda calculus. Unlike others, our implementation allows to reach normal form regardless of interaction net reduction strategy using the approach of so-called token-passing nets. Another new feature is the read-back mechanism also implemented without leaving the formalism of interaction nets.

cs.LO↗

arXiv2015

Macro Lambda Calculus

The goal of our Macro Lambda Calculus project (MLC) is to encode lambda terms into interaction nets. Its software implementation will accept input in the notation similar to lambda calculus allowing macro definitions. Output is similar to interaction calculus and is suitable for our Interaction Nets Compiler program (INC). In this paper, we describe the interaction system for call-by-need evaluation and the mechanism of encoding lambda terms into this system which MLC is based on.

cs.LO↗

arXiv2014

A recursive normalizing one-step reduction strategy for the distributive lambda calculus

We positively answer the question A.1.6 in J. Klop's "Ustica Notes": "Is there a recursive normalizing one-step reduction strategy for micro $λ$-calculus?" Micro $λ$-calculus refers to an implementation of the $λ$-calculus due to Revesz, implementing $β$-reduction by means of "micro steps" recursively distributing a $β$-redex $(λx.M)\ N$ over its body $M$.

cs.LO↗

arXiv2013

Lambda Calculus Synopsis

This text gives a rough, but linear summary covering some key definitions, notations, and propositions from Lambda Calculus: Its Syntax and Semantics, the classical monograph by Barendregt. First, we define a theory of untyped extensional lambda calculus. Then, some syntactic sugar, a system of combinatory logic, and the fixed point theorem are described. The final section introduces a topology on the set of lambda terms which is meant to explain an illusory contradiction. Namely, functions defined on the set of lambda terms are in the set of lambda terms itself, the latter being a countable set. However, the functions on the set of lambda terms appear to be continuous with respect to a topology of trees.

cs.LO↗

arXiv2013

Interaction Nets in Russian

Draft translation to Russian of Chapter 7, Interaction-Based Models of Computation, from Models of Computation: An Introduction to Computability Theory by Maribel Fernandez. "In this chapter, we study interaction nets, a model of computation that can be seen as a representative of a class of models based on the notion of 'computation as interaction'. Interaction nets are a graphical model of computation devised by Yves Lafont in 1990 as a generalisation of the proof structures of linear logic. It can be seen as an abstract formalism, used to define algorithms and analyse their cost, or as a low-level language into which other programming languages can be compiled. This is fruitful because interaction nets can be implemented with reasonable efficiency."

cs.LO↗

arXiv2012

Blind graph rewriting systems

We consider a simple (probably, the simplest) structure for random access memory. This structure can be used to construct a universal system with nearly void processor, namely, we demonstrate that the processor of such a system may have empty instruction set, in a more strong manner than the existing ZISC (zero instruction set computer based on ideas for artificial neural networks) and NISC architecture (no instruction set computing). More precisely, the processor will be forbidden to analyze any information stored in the memory, the latter being the only state of such a machine. This particular paper is to cover an isolated aspect of the idea, specifically, to provide the logical operations embedded into a system without any built-in conditional statements.

cs.LO↗

arXiv2010

Uniform Memory and Serialization for Lambda Calculus

This paper introduces a special type of systems, defines their properties, and then demonstrates that a reduction machine for pure untyped extensional lambda calculus can be implemented as a system of the introduced type. Specifically, we discuss uniform memory as a special kind of graphs and real time operation of state machines that use the uniform memory as their state. Also, we consider a special case of serialization, the latter being useful for the mechanism that compares results during computation, not after the computation is done. However, we start with detailed explanation of our motivation for this work.

cs.LO↗

arXiv2010

The Heap Lambda Machine

This paper introduces a new machine architecture for evaluating lambda expressions using the normal-order reduction, which guarantees that every lambda expression will be evaluated if the expression has its normal form and the system has enough memory. The architecture considered here operates using heap memory only. Lambda expressions are represented as graphs, and all algorithms used in the processing unit of this machine are non-recursive.

cs.LO↗