Expressiveness of Generic Process Shape Types

Shape types are a general concept of process types which work for many process calculi. We extend the previously published Poly* system of shape types to support name restriction. We evaluate the expressiveness of the extended system by showing that shape types are more expressive than an implicitly typed pi-calculus and an explicitly typed Mobile Ambients. We demonstrate that the extended system makes it easier to enjoy advantages of shape types which include polymorphism, principal typings, and a type inference implementation.Comment: Submitted to Trustworthy Global Computing (TGC) 2010

Generic process shape types and the Poly* system

Shape types are a general concept of process types which allows verification of various properties of processes from various calculi. The key property is that shape types “look like processes”, that is, they resemble process structure and content. PolyV, originally designed by Makholm and Wells, is a type system scheme which can be instantiated to a shape type system for many calculi. Every PolyV instantiation has desirable properties including subject reduction, polymorphism, the existence of principal typings, and a type inference algorithm. In the first part of this thesis, we fix and describe inconsistencies found in the original PolyV system, we extend the system to support name restriction, and we provide a detailed proof of the correctness of the system. In the second part, we present a description of the type inference algorithm which we use to constructively prove the existence of principal typings. In the third part, we present various applications of shape types which demonstrate their advantages. Furthermore we prove that shape types can provide the same expressive power as and also strictly superior expressive power than predicates of three quite dissimilar analysis systems from the literature, namely, (1) an implicitly typed π-calculus, (2) an explicitly typed Mobile Ambients, (3) and a flow analysis system for BioAmbients.Engineering and Physical Sciences Research Council (EPSRC) EP/C013573/

A Formal Proof of PAC Learnability for Decision Stumps

We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of classifier. Though such a proof appears simple on paper, analytic and measure-theoretic subtleties arise when carrying it out fully formally. Our proof is structured so as to separate reasoning about deterministic properties of a learning function from proofs of measurability and analysis of probabilities.Comment: 13 pages, appeared in Certified Programs and Proofs (CPP) 202

Hammering Mizar by Learning Clause Guidance (Short Paper)

We describe a very large improvement of existing hammer-style proof automation over large ITP libraries by combining learning and theorem proving. In particular, we have integrated state-of-the-art machine learners into the E automated theorem prover, and developed methods that allow learning and efficient internal guidance of E over the whole Mizar library. The resulting trained system improves the real-time performance of E on the Mizar library by 70% in a single-strategy setting

Recursive Polynomial Reductions for Classical Planning

Reducing accidental complexity in planning problems is a well-established method for increasing efficiency of classical planning. Removal of superfluous facts and actions, and problem transformation by recursive macro actions are representatives of such methods working directly on input planning problems. Despite of its general applicability and thorough theoretical analysis, there is only a sparse amount of experimental results. In this paper, we adopt selected reduction methods from literature and amend them with a generalization-based reduction scheme and auxiliary reductions. We show that all presented reductions are polynomial in time to the size of an input problem. All reductions applied in a recursive manner produce only safe (solution preserving) abstractions of the problem, and they can implicitly represent exponentially long plans in a compact form. Experimentally, we validate efficiency of the presented reductions on the IPC benchmark set and show average 24% reduction over all problems. Additionally, we experimentally analyze the trade-off between increase of coverage and decrease of the plan quality