Program Schemes, Recursion Schemes, and Formal Languages

Higher type recursive program schemes and the nested pushdown automaton

When implementing recursive programs on a standard von Neumann random access machine (RAM) it is natural and well known how to use a pushdown store in order to keep track of the recursive procedure calls when the program runs. The more abstract world of program schemes abounds with examples of this pushdown – recursion relation. As a concrete example it is well known how to implement monadic re...

Computationally secure multiple secret sharing: models, schemes, and formal security analysis

A multi-secret sharing scheme (MSS) allows a dealer to share multiple secrets among a set of participants. in such a way a multi-secret sharing scheme (MSS) allows a dealer to share multiple secrets among a set of participants, such that any authorized subset of participants can reconstruct the secrets. Up to now, existing MSSs either require too long shares for participants to be perfect secur...

Types and Recursion Schemes for Higher-Order Program Verification

Equivalence Problems for Deterministic Context-Free Languages and Monadic Recursion Schemes

In this paper we consider how certain properties of monadic recursion schemes are related to those of cteterministic context-free languages. Previous work showed only how to translate properties of schemes into properties of languages [3]. This was accomplished by a construction that when given any monadic recursion scheme S, produced a deterministic pushdown automaton (abbreviated dpda) accept...

Recursive Program Schemes and Context-Free Monads

Solutions of recursive program schemes over a given signature Σ were characterized by Bruno Courcelle as precisely the context-free (or algebraic) Σ-trees. These are the finite and infinite Σ-trees yielding, via labelling of paths, context-free languages. Our aim is to generalize this to finitary endofunctors H of general categories: we construct a monad CH “generated” by solutions of recursive...