Related papers: On the complexity of the correctness problem for n…
There are two ways to check if a program is correct, namely execute it or review it. While executing a program is the ultimate test for its correctness reviewing the program can occur earlier in its development and find problems if done…
The goal of the paper is to relate complexity measures associated with the evaluation of Boolean functions (certificate complexity, decision tree complexity) and learning dimensions used to characterize exact learning (teaching dimension,…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
Large language models have shown that impressive zero-shot performance can be achieved through natural language prompts (Radford et al., 2019; Brown et al., 2020; Sanh et al., 2021). Creating an effective prompt, however, requires…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
Students sometimes produce code that works but that its author does not comprehend. For example, a student may apply a poorly-understood code template, stumble upon a working solution through trial and error, or plagiarize. Similarly,…
Numerical software are widely used in safety-critical systems such as aircrafts, satellites, car engines and so on, facilitating dynamics control of such systems in real time, it is therefore absolutely necessary to verify their…
Contribution: This study examined student effort and performance in an introductory programming course with respect to student-held implicit theories and self-efficacy. Background: Implicit theories and self-efficacy shed a light into…
Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
We present a new procedure to infer size bounds for integer programs automatically. Size bounds are important for the deduction of bounds on the runtime complexity or in general, for the resource analysis of programs. We show that our…
Large language models possess impressive capabilities in generating programs (e.g., Python) from natural language descriptions to execute robotic tasks. However, these generated programs often contain errors that violate externally given…
Suppose we are given two probability measures on the set of one-way infinite finite-alphabet sequences and consider the question when one of the measures predicts the other, that is, when conditional probabilities converge (in a certain…
Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…
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…
We study sequential programs that are instruction sequences with dynamically instantiated instructions. We define the meaning of such programs in two different ways. In either case, we give a translation by which each program with…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…
Each Boolean function can be computed by a single-pass instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction. Auxiliary Boolean…
Software, while beneficial, poses potential cybersecurity risks due to inherent vulnerabilities. Detecting these vulnerabilities is crucial, and deep learning has shown promise as an effective tool for this task due to its ability to…