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Constrained Horn Clauses (CHCs) are often used in automated program verification. Thus, techniques for (dis-)proving satisfiability of CHCs are a very active field of research. On the other hand, acceleration techniques for computing…
A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
Recent advancements in large language models (LLMs) underscore the need for stronger reasoning capabilities to solve complex problems effectively. While Chain-of-Thought (CoT) reasoning has been a step forward, it remains insufficient for…
We expose in a tutorial fashion the mechanisms which underlie the synthesis of optimization algorithms based on dynamic integral quadratic constraints. We reveal how these tools from robust control allow to design accelerated gradient…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
Deep Reinforcement Learning (RL) has demonstrated impressive results in solving complex robotic tasks such as quadruped locomotion. Yet, current solvers fail to produce efficient policies respecting hard constraints. In this work, we…
We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may…
We present a new data structure called the \emph{Compressed Random Access Memory} (CRAM) that can store a dynamic string $T$ of characters, e.g., representing the memory of a computer, in compressed form while achieving asymptotically…
Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a…
We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the…
Concurrent Constraint Programming (CCP) is a simple and powerful model for concurrency where agents interact by telling and asking constraints. Since their inception, CCP-languages have been designed for having a strong connection to logic.…
Model-driven software engineering is a suitable method for dealing with the ever-increasing complexity of software development processes. Graphs and graph transformations have proven useful for representing such models and changes to them.…
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…
Graph transformation systems (GTS) and constraint handling rules (CHR) are non-deterministic rule-based state transition systems. CHR is well-known for its powerful confluence and program equivalence analyses, for which we provide the basis…
We build on a recently proposed method for explaining solutions of constraint satisfaction problems. An explanation here is a sequence of simple inference steps, where the simplicity of an inference step is measured by the number and types…
In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…
Data replication is used in distributed systems to maintain up-to-date copies of shared data across multiple computers in a network. However, despite decades of research, algorithms for achieving consistency in replicated systems are still…