Related papers: On algorithmic equivalence of instruction sequence…
Some techniques for the use of bitwise operations are described in the article. As an example, an open problem of isomorphism-free generations of combinatorial objects is discussed. An equivalence relation on the set of square binary…
Instruction data is crucial for improving the capability of Large Language Models (LLMs) to align with human-level performance. Recent research LIMA demonstrates that alignment is essentially a process where the model adapts instructions'…
Several measures exist for string similarity, including notable ones like the edit distance and the indel distance. The former measures the count of insertions, deletions, and substitutions required to transform one string into another,…
Morphic sequences form a natural class of infinite sequences, typically defined as the coding of a fixed point of a morphism. Different morphisms and codings may yield the same morphic sequence. This paper investigates how to prove that two…
Active learning algorithms select a subset of data for annotation to maximize the model performance on a budget. One such algorithm is Expected Gradient Length, which as the name suggests uses the approximate gradient induced per example in…
We present an algorithm for approximating semidefinite programs with running time that is sublinear in the number of entries in the semidefinite instance. We also present lower bounds that show our algorithm to have a nearly optimal running…
We show that one can decide if a rational equivalence relation can be given as the equivalence kernel of a sequential letter-to-letter transduction. This problem comes from the setting of games with imperfect information. In [1, p. 6] the…
For a finite binary string $x$ its logical depth $d$ for significance $b$ is the shortest running time of a program for $x$ of length $K(x)+b$. There is another definition of logical depth. We give a new proof that the two versions are…
The execution of concurrent programs generally involves some degree of nondeterminism, mostly due to the relative speeds of the concurrent processes. As a consequence, reproducibility is often challenging. This problem has been…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at…
We define focus-method interfaces and some connections between such interfaces and instruction sequences, giving rise to instruction sequence components. We provide a flexible and practical notation for interfaces using an abstract datatype…
The $\pi$-calculus is used as a model for programming languages. Its contexts exhibit arbitrary concurrency, making them very discriminating. This may prevent validating desirable behavioural equivalences in cases when more disciplined…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…
This paper describes an algorithm for the computation of FIRST and FOLLOW sets for use with feature-theoretic grammars in which the value of the sets consists of pairs of feature-theoretic categories. The algorithm preserves as much…
A string diagram is a two-dimensional graphical representation that can be described as a one-dimensional term generated from a set of primitives using sequential and parallel compositions. Since different syntactic terms may represent the…
Continual (sequential) training and multitask (simultaneous) training are often attempting to solve the same overall objective: to find a solution that performs well on all considered tasks. The main difference is in the training regimes,…
By the recent advances in computer technology leading to the invention of more powerful processors, the importance of creating models using data training is even greater than ever. Given the significance of this issue, this work tries to…