Algorithms for Extended Alpha-Equivalence and Complexity

Equality of expressions in lambda-calculi, higher-order programming languages, higher-order programming calculi and process calculi is defined as alpha-equivalence. Permutability of bindings in let-constructs and structural congruence axioms extend alpha-equivalence. We analyse these extended alpha-equivalences and show that there are calculi with polynomial time algorithms, that a multiple-binding “let ” may make alpha-equivalence as hard as finding graph-isomorphisms, and that the replication operator in the pi-calculus may lead to an EXPSPACE-hard alpha-equivalence problem

User-centric secure cross-site interaction framework for online social networking services

Social networking service is one of major technological phenomena on Web 2.0. Hun- dreds of millions of users are posting message, photos, and videos on their profiles and interacting with other users, but the sharing and interaction are limited within the same social networking site. Although users can share some content on a social networking site with people outside of the social networking sites using a public references to their content, appropriate access control mechanisms are not supported. In this dissertation, we outline a cross-site interaction framework and identity mapping approaches that enable social net- work users to share their content across social networking sites. We propose a cross-site interaction framework x-mngr, allowing users to interact with others on other social net- working sites, with a cross-site access control policy. We also propose identity-mapping approaches that map user’s identities across social networking sites. The partial mapping approach based on a supervised learning mechanism which provides user’s identity map- ping based on a training set composed of a small subset of the profile mappings. We provide mechanisms to enable users to fuse identity-mapping decisions that are provided by their friends or others on the social network. Furthermore, we propose a Game With A Purpose (GWAP) approach that provides identity-mappings using a social network game. The proposed framework and game are implemented on real social networking sites such as Facebook and MySpace. The experiments are performed to evaluate the feasibility of our approaches. A user study is also performed and the result is included as part of our evaluation efforts for the proposed framework

A System of Interaction and Structure III: The Complexity of BV and Pomset Logic

Pomset logic and BV are both logics that extend multiplicative linear logic (with Mix) with a third connective that is self-dual and non-commutative. Whereas pomset logic originates from the study of coherence spaces and proof nets, BV originates from the study of series-parallel orders, cographs, and proof systems. Both logics enjoy a cut-admissibility result, but for neither logic can this be done in the sequent calculus. Provability in pomset logic can be checked via a proof net correctness criterion and in BV via a deep inference proof system. It has long been conjectured that these two logics are the same. In this paper we show that this conjecture is false. We also investigate the complexity of the two logics, exhibiting a huge gap between the two. Whereas provability in BV is NP-complete, provability in pomset logic is $\Sigma_2^p$-complete. We also make some observations with respect to possible sequent systems for the two logics

A Term Equality Problem Equivalent to Graph Isomorphism

We demonstrate that deciding if two terms containing otherwise uninterpreted associative, commutative, and associative-commutative function symbols and commutative variable-binding operators are equal is polynomially equivalent to determining if two graphs are isomorphic. The reductions we use provide insight into this result and suggest polynomial time special cases. Key Words: Automatic Theorem Proving, Computational Complexity, Equality Reasoning, Graph Isomorphism. 1 Introduction Decision procedures for equality play an important role in automated theorem proving. We examine the complexity of a specific problem in equality reasoning: determining if two terms, which possibly contain associative, commutative, and associative-commutative (AC) functions and commutative variable-binding operators (that is, adjacent operators may be swapped) are equal. We prove that this problem is polynomially equivalent to deciding if two graphs are isomorphic. The exact complexity of graph isomorphi..