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Joshua Schneider

Publications and source records attributed to Joshua Schneider.

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Policy Change for Treelike Monitors

We study the policy change problem that arises in the runtime verification of long-running systems. The online monitors typically used in this context are generally treelike, in that they maintain substates that monitor subformulae of the target policy. We consider when and how the policy can be changed while the monitored system is running by only exploiting the information stored in the monitor's state. This is relevant, for example, to account for new system functionality or changes in regulatory requirements. We formally define the policy change problem in a general setting, independent of any specific (treelike) monitor implementation. We then show that policy change for past-time metric temporal logic (pMTL) is decidable but has tight non-primitive recursive lower and upper bounds, while with discrete-time semantics it is EXPSPACE-complete.

cs.LO

Quotients of Bounded Natural Functors

The functorial structure of type constructors is the foundation for many definition and proof principles in higher-order logic (HOL). For example, inductive and coinductive datatypes can be built modularly from bounded natural functors (BNFs), a class of well-behaved type constructors. Composition, fixpoints, and, under certain conditions, subtypes are known to preserve the BNF structure. In this article, we tackle the preservation question for quotients, the last important principle for introducing new types in HOL. We identify sufficient conditions under which a quotient inherits the BNF structure from its underlying type. Surprisingly, lifting the structure in the obvious manner fails for some quotients, a problem that also affects the quotients of polynomial functors used in the Lean proof assistant. We provide a strictly more general lifting scheme that supports such problematic quotients. We extend the Isabelle/HOL proof assistant with a command that automates the registration of a quotient type as a BNF, reducing the proof burden on the user from the full set of BNF axioms to our inheritance conditions. We demonstrate the command's usefulness through several case studies.

cs.LO