Related papers: Step-Indexed Relational Reasoning for Countable No…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
As is evident in the programming language literature, many practitioners favor specifying dynamic program behavior using big-step over small-step semantics. Unlike small-step semantics, which must dwell on every intermediate program state,…
We present an approach to program reasoning which inserts between a program and its verification conditions an additional layer, the denotation of the program expressed in a declarative form. The program is first translated into its…
The compactness lemma in programming language theory states that any recursive function can be simulated by a finite unrolling of the function. One important use case it has is in the logical relations proof technique for proving properties…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
Although contemporary large language models (LMs) demonstrate impressive question-answering capabilities, their answers are typically the product of a single call to the model. This entails an unwelcome degree of opacity and compromises…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Mathematical reasoning has been challenging for large language models (LLMs), and the introduction of step-by-step Chain-of-Thought (CoT) inference has significantly advanced the mathematical capabilities of LLMs. However, current…
Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying…
We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we consider cons-free programs of varying data orders, equipped with explicit non-deterministic choice.…
Two natural decision problems regarding the XML query language XQuery are well-definedness and semantic type-checking. We study these problems in the setting of a relational fragment of XQuery. We show that well-definedness and semantic…
Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…
Large language models make remarkable progress in reasoning capabilities. Existing works focus mainly on deductive reasoning tasks (e.g., code and math), while another type of reasoning mode that better aligns with human learning, inductive…
Formal semantics provides rigorous, mathematically precise definitions of programming languages, with which we can argue about program behaviour and program equivalence by formal means; in particular, we can describe and verify our…
The notion of a non-deterministic logical matrix (where connectives are interpreted as multi-functions) extends the traditional semantics for propositional logics based on logical matrices (where connectives are interpreted as functions).…
Evaluation of reasoning language models gained importance after it was observed that they can combine their existing capabilities into novel traces of intermediate steps before task completion and that the traces can sometimes help them to…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
The model of asynchronous programming arises in many contexts, from low-level systems software to high-level web programming. We take a language-theoretic perspective and show general decidability and undecidability results for asynchronous…
A linear ordering is called context-free if it is the lexicographic ordering of some context-free language and is called scattered if it has no dense subordering. Each scattered ordering has an associated ordinal, called its rank. It is…
We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of…