Related papers: Periodic Single-Pass Instruction Sequences
We propose a novel method for automatic program synthesis. P-Tree Programming represents the program search space through a single probabilistic prototype tree. From this prototype tree we form program instances which we evaluate on a given…
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…
Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…
The sequential composition of propositional logic programs has been recently introduced. This paper studies the sequential {\em decomposition} of programs by studying Green's relations $\mathcal{L,R,J}$ -- well-known in semigroup theory --…
This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later…
Due to their quantitative nature, probabilistic programs pose non-trivial challenges for designing compositional and efficient program analyses. Many analyses for probabilistic programs rely on iterative approximation. This article presents…
A re-construction of the fundamentals of programming as a small mathematical theory (PRISM) based on elementary set theory. Highlights: $\bullet$ Zero axioms. No properties are assumed, all are proved (from standard set theory). $\bullet$ A…
A steering fragment of an instruction sequence consists of a sequence of steering instructions. These are decision points involving the check of a propositional statement in sequential logic. The question is addressed why composed…
We develop theory concerning non-uniform complexity in a setting in which the notion of single-pass instruction sequence considered in program algebra is the central notion. We define counterparts of the complexity classes P/poly and…
A circular program contains a data structure whose definition is self-referential or recursive. The use of such a definition allows efficient functional programs to be written and can avoid repeated evaluations and the creation of…
Backpropagation is a classic automatic differentiation algorithm computing the gradient of functions specified by a certain class of simple, first-order programs, called computational graphs. It is a fundamental tool in several fields, most…
The notion of transducer integer sequences is considered through a series of examples. By definition, transducer integer sequences are integer sequences produced, under a suitable interpretation, by finite automata encoding tree morphisms…
Program behavior may depend on parameters, which are either configured before compilation time, or provided at run-time, e.g., by sensors or other input devices. Parametric program analysis explores how different parameter settings may…
How do neural networks trained over sequences acquire the ability to perform structured operations, such as arithmetic, geometric, and algorithmic computation? To gain insight into this question, we introduce the sequential group…
Pivoting methods are of vital importance for linear programming, the simplex method being the by far most well-known. In this paper, a primal-dual pair of linear programs in canonical form is considered. We show that there exists a sequence…
Program synthesis is a class of regression problems where one seeks a solution, in the form of a source-code program, mapping the inputs to their corresponding outputs exactly. Due to its precise and combinatorial nature, program synthesis…
Studies of issues related to computability and computational complexity involve the use of a model of computation. Pivotal to such a model are the computational processes considered. Processes of this kind can be described using an…
Asynchronous programming has appeared as a programming style that overcomes undesired properties of concurrent programming. Typically in asynchronous models of programming, methods are posted into a post list for latter execution. The order…
Linear Programs (LP) are celebrated widely, particularly so in machine learning where they have allowed for effectively solving probabilistic inference tasks or imposing structure on end-to-end learning systems. Their potential might seem…
Semantics of logic programs has been given by proof theory, model theory and by fixpoint of the immediate-consequence operator. If clausal logic is a programming language, then it should also have a compositional semantics. Compositional…