Related papers: Strong Bisimulation for Control Operators
To improve the performance and explainability of LLM-based natural language reasoning, structured reasoning can be applied to generate explicitly structured proofs. Among different methods for structured reasoning, we specifically focus on…
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…
Machine learning algorithms are commonly specified in linear algebra (LA). LA expressions can be rewritten into more efficient forms, by taking advantage of input properties such as sparsity, as well as program properties such as common…
The $\lambda\mu$-calculus plays a central role in the theory of programming languages as it extends the Curry-Howard correspondence to classical logic. A major drawback is that it does not satisfy B\"ohm's Theorem and it lacks the…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
Strong equivalence is a well-studied and important concept in answer set programming (ASP). $\rm LP^{MLN}$ is a probabilistic extension of answer set programs with the weight scheme adapted from Markov Logic. Because of the semantic…
I present a model of universal parallel computation called $\Delta$-Nets, and a method to translate $\lambda$-terms into $\Delta$-nets and back. Together, the model and the method constitute an algorithm for optimal parallel…
A bilevel program is an optimization problem whose constraints involve another optimization problem. This paper studies bilevel polynomial programs (BPPs), i.e., all the functions are polynomials. We reformulate BPPs equivalently as…
We investigate the concept of strong equivalence within the extended framework of Answer Set Programming with constraints. Two groups of rules are considered strongly equivalent if, informally speaking, they have the same meaning in any…
The connection between control algorithms for Markov decision processes and optimization algorithms has been implicitly and explicitly exploited since the introduction of dynamic programming algorithm by Bellman in the 1950s. Recently, this…
Higher-order abstract GSOS is a recent extension of Turi and Plotkin's framework of Mathematical Operational Semantics to higher-order languages. The fundamental well-behavedness property of all specifications within the framework is that…
This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The…
State minimization of combinatorial filters is a fundamental problem that arises, for example, in building cheap, resource-efficient robots. But exact minimization is known to be NP-hard. This paper conducts a more nuanced analysis of this…
We give an algebraic characterization of the syntax and semantics of a class of languages with variable binding. We introduce a notion of 2-signature: such a signature specifies not only the terms of a language, but also reduction rules on…
We present an SMT-based symbolic model checking algorithm for safety verification of recursive programs. The algorithm is modular and analyzes procedures individually. Unlike other SMT-based approaches, it maintains both "over-" and…
Reactive systems (RSs) represent a meta-framework aimed at deriving behavioral congruences for those computational formalisms whose operational semantics is provided by reduction rules. RSs proved a flexible specification device, yet so far…
We investigate how various forms of bisimulation can be characterised using the technology of logical relations. The approach taken is that each form of bisimulation corresponds to an algebraic structure derived from a transition system,…
We study coupled logical bisimulation (CLB) to reason about contextual equivalence in the lambda-calculus. CLB originates in a work by Dal Lago, Sangiorgi and Alberti, as a tool to reason about a lambda-calculus with probabilistic…
We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…
Motivated by partition regularity problems of homogeneous quadratic equations, we prove multiple recurrence and convergence results for multiplicative measure preserving actions with iterates given by rational sequences involving…