Related papers: Expressiveness and Extensions of an Instruction Se…
A program is a finite piece of data that produces a (possibly infinite) sequence of primitive instructions. From scratch we develop a linear notation for sequential, imperative programs, using a familiar class of primitive instructions and…
We study sequential programs that are instruction sequences with jump-shift instructions in the setting of PGA (ProGram Algebra). Jump-shift instructions preceding a jump instruction increase the position to jump to. The jump-shift…
We introduce an algebra of instruction sequences by presenting a semigroup C in which programs can be represented without directional bias: in terms of the next instruction to be executed, C has both forward and backward instructions and a…
PGA (ProGram Algebra) is an algebra of programs which concerns programs in their simplest form: sequences of instructions. Molecular dynamics is a simple model of computation developed in the setting of PGA, which bears on the use of…
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…
Parsing Expression Grammars (PEGs) are a formalism that can describe all deterministic context-free languages through a set of rules that specify a top-down parser for some language. PEGs are easy to use, and there are efficient…
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…
Parsing Expression Grammars (PEGs) define languages by specifying recursive-descent parser that recognises them. The PEG formalism exhibits desirable properties, such as closure under composition, built-in disambiguation, unification of…
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…
What is the best representation for doing euclidean geometry on computers? These notes from a SIGGRAPH 2019 short course entitled "Geometric algebra for computer graphics" introduce projective geometric algebra (PGA) as a modern framework…
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…
The program dependence graph (PDG) represents data and control dependence between statements in a program. This paper presents an operational semantics of program dependence graphs. Since PDGs exclude artificial order of statements that…
We show that if PGA is understood as a subalgebra of CGA in mathematically correct sense, then the flat objects share the same representation in PGA and CGA. Particularly, we treat duality in PGA. This leads to unification of PGA and CGA…
One common belief is that with complex models and pre-training on large-scale datasets, transformer-based methods for referring expression comprehension (REC) perform much better than existing graph-based methods. We observe that since most…
A compiler's intermediate representation (IR) defines a program's execution plan by encoding its instructions and their relative order. Compiler optimizations aim to replace a given execution plan with a semantically-equivalent one that…
Graph neural networks (GNNs) have emerged as a powerful tool for learning software engineering tasks including code completion, bug finding, and program repair. They benefit from leveraging program structure like control flow graphs, but…
Parsing Expression Grammars (PEGs) describe top-down parsers. Unfortunately, the error-reporting techniques used in conventional top-down parsers do not directly apply to parsers based on Parsing Expression Grammars (PEGs), so they have to…
GP (for Graph Programs) is a rule-based, nondeterministic programming language for solving graph problems at a high level of abstraction, freeing programmers from handling low-level data structures. The core of GP consists of four…
It is natural for probabilistic programs to use conditionals to express alternative substructures in models, and loops (recursion) to express repeated substructures in models. Thus, probabilistic programs with conditionals and recursion…
PEGs were formalized by Ford in 2004, and have several pragmatic operators (such as ordered choice and unlimited lookahead) for better expressing modern programming language syntax. Since these operators are not explicitly defined in the…