Graph-Based Shape Analysis Beyond Context-Freeness

We develop a shape analysis for reasoning about relational properties of data structures. Both the concrete and the abstract domain are represented by hypergraphs. The analysis is parameterized by user-supplied indexed graph grammars to guide concretization and abstraction. This novel extension of context-free graph grammars is powerful enough to model complex data structures such as balanced binary trees with parent pointers, while preserving most desirable properties of context-free graph grammars. One strength of our analysis is that no artifacts apart from grammars are required from the user; it thus offers a high degree of automation. We implemented our analysis and successfully applied it to various programs manipulating AVL trees, (doubly-linked) lists, and combinations of both

Generating Bijections between HOAS and the Natural Numbers

A provably correct bijection between higher-order abstract syntax (HOAS) and the natural numbers enables one to define a "not equals" relationship between terms and also to have an adequate encoding of sets of terms, and maps from one term family to another. Sets and maps are useful in many situations and are preferably provided in a library of some sort. I have released a map and set library for use with Twelf which can be used with any type for which a bijection to the natural numbers exists. Since creating such bijections is tedious and error-prone, I have created a "bijection generator" that generates such bijections automatically together with proofs of correctness, all in the context of Twelf.Comment: In Proceedings LFMTP 2010, arXiv:1009.218

A Tractable Extension of Linear Indexed Grammars

It has been shown that Linear Indexed Grammars can be processed in polynomial time by exploiting constraints which make possible the extensive use of structure-sharing. This paper describes a formalism that is more powerful than Linear Indexed Grammar, but which can also be processed in polynomial time using similar techniques. The formalism, which we refer to as Partially Linear PATR manipulates feature structures rather than stacks.Comment: 8 pages LaTeX, uses eaclap.sty, to appear in EACL-9

From indexed grammars to generating functions

We extend the Chomsky/Sch\"utzenberger method of computing the growth series of an unambiguous context-free language to the larger class of indexed languages. We illustrate the technique with numerous examples.Comment: 23 pages, 3 figure

Modelling Combinatorial Auctions in Linear Logic

We show that linear logic can serve as an expressive framework in which to model a rich variety of combinatorial auction mechanisms. Due to its resource-sensitive nature, linear logic can easily represent bids in combinatorial auctions in which goods may be sold in multiple units, and we show how it naturally generalises several bidding languages familiar from the literature. Moreover, the winner determination problem, i.e., the problem of computing an allocation of goods to bidders producing a certain amount of revenue for the auctioneer, can be modelled as the problem of finding a proof for a particular linear logic sequent