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We propose a framework for verifiable and compositional reinforcement learning (RL) in which a collection of RL subsystems, each of which learns to accomplish a separate subtask, are composed to achieve an overall task. The framework…
Term rewriting is a Turing complete model of computation. When taught to students of computer science, key properties of computation as well as techniques to analyze programs on an abstract level are conveyed. This paper gives a swift…
Boyer and Moore have discussed a recursive function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
Through reinforcement learning (RL) with outcome correctness rewards, large reasoning models (LRMs) with scaled inference computation have demonstrated substantial success on complex reasoning tasks. However, the one-sided reward, focused…
We propose a method to write and check a specification including quantifiers using behaviors, i.e., input-output pairs. Our method requires the following input from the user: (1) answers to a finite number of queries, each of which presents…
Recently, many techniques have been introduced that allow the (automated) classification of the runtime complexity of term rewrite systems (TRSs for short). In earlier work, the authors have shown that for confluent TRSs, innermost…
This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus,…
The term {\em meta-programming} refers to the ability of writing programs that have other programs as data and exploit their semantics. The aim of this paper is presenting a methodology allowing us to perform a correct termination analysis…
We propose a framework for verifiable and compositional reinforcement learning (RL) in which a collection of RL subsystems, each of which learns to accomplish a separate subtask, are composed to achieve an overall task. The framework…
Non-confluent and non-terminating constructor-based term rewrite systems are useful for the purpose of specification and programming. In particular, existing functional logic languages use such kind of rewrite systems to define possibly…
An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of…
In this article we investigate how a subterm pattern matching algorithm can be exploited to implement efficient term rewriting procedures. From the left-hand sides of the rewrite system we construct a set automaton, which can be used to…
We study the recursion-theoretic complexity of Positive Almost-Sure Termination ($\mathsf{PAST}$) in an imperative programming language with rational variables, bounded nondeterministic choice, and discrete probabilistic choice. A program…
The central challenge of reinforcement learning for reasoning lies not only in the sparsity of outcome-level supervision, but more fundamentally in how to transform feedback provided only at the end of a sequence into fine-grained learning…
Inconsistent values are commonly encountered in real-world applications, which can negatively impact data analysis and decision-making. While existing research primarily focuses on identifying the smallest removal set to resolve…
We study active integrity constraints and revision programming, two formalisms designed to describe integrity constraints on databases and to specify policies on preferred ways to enforce them. Unlike other more commonly accepted…
The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful…
Formal verification of a software system relies on formalising the requirements to which it should adhere, which can be challenging. While formalising requirements from natural-language, we have dependencies that lead to duplication of…
On the one hand, checking specific termination proofs by hand, say using a particular collection of matrix interpretations, can be an arduous and error-prone task. On the other hand, automation of such checks would save time and help to…