Related papers: Lean and Full Congruence Formats for Recursion
Numerous confluence criteria for plain term rewrite systems are known. For logically constrained rewrite system, an attractive extension of term rewriting in which rules are equipped with logical constraints, much less is known. In this…
Reactive systems \`a la Leifer and Milner, an abstract categorical framework for rewriting, provide a suitable framework for deriving bisimulation congruences. This is done by synthesizing interactions with the environment in order to…
Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical…
We study bisimulation and context equivalence in a probabilistic $\lambda$-calculus. The contributions of this paper are threefold. Firstly we show a technique for proving congruence of probabilistic applicative bisimilarity. While the…
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…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
Coherence is an essential property of well-written texts, that refers to the way textual units relate to one another. In the era of generative AI, coherence assessment is essential for many NLP tasks; summarization, generation, long-form…
In the framework of logic labelled transition system, a variant of weak ready simulation has been presented by L\"{u}ttgen and Vogler. It has been shown that such behavioural preorder is the largest precongruence w.r.t parallel and…
Correctness conditions for concurrent objects describe how atomicity of an abstract sequential object may be decomposed. Many different concurrent objects and proof methods for them have been developed. However, arguments about correctness…
Logically constrained term rewriting is a relatively new rewriting formalism that naturally supports built-in data structures, such as integers and bit vectors. In the analysis of logically constrained term rewrite systems (LCTRSs),…
Often, when analyzing the behaviour of systems modelled as context-free languages, we wish to know if two languages overlap. To this end, we present an effective semi-decision procedure for regular separability of context-free languages,…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
Causal-consistent reversibility is the reference notion of reversibility for concurrency. We introduce a modular framework for defining causal-consistent reversible extensions of concurrent models and languages. We show how our framework…
We show that the language equivalence problem for regular and context-free commutative grammars is coNEXP-complete. In addition, our lower bound immediately yields further coNEXP-completeness results for equivalence problems for…
Proofs of coherence in category theory, starting from Mac Lane's original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what one finds in the lambda calculus, or in term-rewriting…
In this paper, we study the regularity assumptions commonly adopted in bilevel optimization with constrained lower-level problems, including the linear independence constraint qualification, the strict complementary slackness condition, and…
Most language models (LMs) are trained and applied in an autoregressive left-to-right fashion, assuming that the next token only depends on the preceding ones. However, this assumption ignores the potential benefits of using the full…
Contextual equivalence equate terms that have the same observable behaviour in any context. A standard contextual equivalence for CCS is the strong barbed congruence. Configuration structures are a denotational semantics for processes in…
In this work we formulate the problem of satisfying a linear temporal logic formula on a linear plant with output feedback, through a recent hybrid systems formalism. We relate this problem to the notion of recurrence introduced for the…
Reversible systems feature both forward computations and backward computations, where the latter undo the effects of the former in a causally consistent manner. The compositionality properties and equational characterizations of strong and…