Related papers: On instruction sets for Boolean registers in progr…
Register allocation is a much studied problem. A particularly important context for optimizing register allocation is within loops, since a significant fraction of the execution time of programs is often inside loop code. A variety of…
Applying deep learning to solve real-life instances of hard combinatorial problems has tremendous potential. Research in this direction has focused on the Boolean satisfiability (SAT) problem, both because of its theoretical centrality and…
Automating algorithm configuration is growing increasingly necessary as algorithms come with more and more tunable parameters. It is common to tune parameters using machine learning, optimizing performance metrics such as runtime and…
Large language models (LLMs) have demonstrated remarkable abilities in representation learning for program synthesis and understanding tasks. The quality of the learned representations appears to be dictated by the neural scaling laws as a…
Instruction subsets (ISs) are heuristics that can shrink the size of the inductive programming (IP) search space by tens of orders of magnitude. Here, we extend the IS approach by introducing instruction and solution probabilities as…
It is shown that the counting function of n Boolean variables can be implemented with the formulae of size O(n^3.06) over the basis of all 2-input Boolean functions and of size O(n^4.54) over the standard basis. The same bounds follow for…
Large Language Models are traditionally finetuned on large instruction datasets. However recent studies suggest that small, high-quality datasets can suffice for general purpose instruction following. This lack of consensus surrounding…
Instruction subsets are heuristics that can reduce the size of the inductive programming search space by tens of orders of magnitude. Comprising many overlapping subsets of different sizes, they serve as predictions of the instructions…
This article provides a survey of circuit complexity bounds for basic boolean transforms exploited in digital circuit design and efficient methods for synthesizing such circuits. The exposition covers structurally simple functions and…
The increasing complexity of modern deep neural network models and the expanding sizes of datasets necessitate the development of optimized and scalable training methods. In this white paper, we addressed the challenge of efficiently…
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 construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…
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…
We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…
Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search…
We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A >>Cohen algebra<< is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of…
There exist several approaches to infer runtime or resource bounds for integer programs automatically. In this paper, we study the subclass of periodic rational solvable loops (prs-loops), where questions regarding the runtime and the size…
Recent work on mini-batch consistency (MBC) for set functions has brought attention to the need for sequentially processing and aggregating chunks of a partitioned set while guaranteeing the same output for all partitions. However, existing…
We propose a calculus of string diagrams to reason about satisfiability of Boolean formulas, and prove it to be sound and complete. We then showcase our calculus in a few case studies. First, we consider SAT-solving. Second, we consider…
What factors contribute to the relative success and corresponding difficulties of in-context learning for Large Language Models (LLMs)? Drawing on insights from the literature on human concept learning, we test LLMs on carefully designed…