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Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator…
The logic of the hide and seek game LHS was proposed to reason about search missions and interactions between agents in pursuit-evasion environments. As proved in literature, having an equality constant in the language of LHS drastically…
Current approaches for formal verification of algorithms face important limitations. For specification, they cannot express algorithms naturally and concisely, especially for algorithms with states and flexible control flow. For…
Many-to-many matching with contracts is studied in the framework of revealed preferences. All preferences are described by choice functions that satisfy natural conditions. Under a no-externality assumption individual preferences can be…
Abstract separation logics are a family of extensions of Hoare logic for reasoning about programs that manipulate resources such as memory locations. These logics are "abstract" because they are independent of any particular concrete…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Logic programming is sometimes described as relational programming: a paradigm in which the programmer specifies and composes n-ary relations using systems of constraints. An advanced logic programming environment will provide tools that…
Contextual refinement and separation logics are successful verification techniques that are very different in nature. First, the former guarantees behavioral refinement between a concrete program and an abstract program while the latter…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
A representation theorem relates different mathematical structures by providing an isomorphism between them: that is, a one-to-one correspondence preserving their original properties. Establishing that the two structures substantially…
Concurrent separation logics have helped to significantly simplify correctness proofs for concurrent data structures. However, a recurring problem in such proofs is that data structure abstractions that work well in the sequential setting…
One of the most attractive features of untyped languages is the flexibility in term creation and manipulation. However, with such power comes the responsibility of ensuring the correctness of these operations. A solution is adding run-time…
Choreographic programming is a paradigm where a concurrent or distributed system is developed in a top-down fashion. Programs, called choreographies, detail the desired interactions between processes, and can be compiled to distributed…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
We give a rigorous framework for the interaction of physical computing devices with abstract computation. Device and program are mediated by the non-logical 'representation relation'; we give the conditions under which representation and…
The proposed framework provides a general model of concurrent imperative programming. Programs are modeled as formal languages and concurrency as an interleaving (or shuffle) operator. This yields a simple and elegant algebra of programs.…
This paper provides a systematic account of the hidden variable models (HVMs) formulated to describe systems of random variables with mutually exclusive contexts. Any such system can be described either by a model with free choice but…
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…
Great advances in program analysis would be enabled if it were possible to derive the function of a program from inputs to outputs (or from initial states to final states, depending on how we model program semantics). Efforts to do so have…