Related papers: Instruction sequence size complexity of parity
In previous work carried out in the setting of program algebra, including work in the area of instruction sequence size complexity, we chose instruction sets for Boolean registers that contain only instructions of a few of the possible…
Every partial function from bit strings of a given length to bit strings of a possibly different given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers,…
For each function on bit strings, its restriction to bit strings of any given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump…
A parameterized algebraic theory of instruction sequences, objects that represent the behaviours produced by instruction sequences under execution, and objects that represent the behaviours exhibited by the components of the execution…
For each function on bit strings, its restriction to bit strings of any given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump…
We perceive programs as single-pass instruction sequences. A single-pass instruction sequence under execution is considered to produce a behaviour to be controlled by some execution environment. Threads as considered in basic thread algebra…
This paper concerns the question to what extent it can be efficiently determined whether an arbitrary program correctly solves a given problem. This question is investigated with programs of a very simple form, namely instruction sequences,…
Parity functions are fundamental Boolean operations with critical applications across machine learning, cryptography, and error correction. Yet, learning high-dimensional parity functions poses significant challenges: in a general setting,…
Instruction sequences with direct and indirect jump instructions are as expressive as instruction sequences with direct jump instructions only. We show that, in the case where the number of instructions is not bounded, we are faced with…
Inductive programming frequently relies on some form of search in order to identify candidate solutions. However, the size of the search space limits the use of inductive programming to the production of relatively small programs. If we…
We investigate the expressiveness of backward jumps in a framework of formalized sequential programming called program algebra. We show that - if expressiveness is measured in terms of the computability of partial Boolean functions - then…
The secure hash function SHA-256 is a function on bit strings. This means that its restriction to the bit strings of any given length can be computed by a finite instruction sequence that contains only instructions to set and get the…
The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to…
Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…
We present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction…
The execution of sequential programs allows them to be represented using mathematical functions formed by the composition of statements following one after the other. Each such statement is in itself a partial function, which allows only…
In this article, we continue our study on universal learning machine by introducing new tools. We first discuss boolean function and boolean circuit, and we establish one set of tools, namely, fitting extremum and proper sampling set. We…
We consider the problem of linearizing a pseudo-Boolean function $f : \{0,1\}^n \to \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This…
Finding the optimal pass sequence of compilation can lead to a significant reduction in program size and/or improvement in program efficiency. Prior works on compilation pass ordering have two major drawbacks. They either require an…
We are considering RAMs $N_{n}$, with wordlength $n=2^{d}$, whose arithmetic instructions are the arithmetic operations multiplication and addition modulo $2^{n}$, the unary function $ \min\lbrace 2^{x}, 2^{n}-1\rbrace$, the binary…