Beautiful Structures: An Appreciation of the Contributions of Alan Selman

Professor Alan Selman has been a giant in the field of computational complexity for the past forty years. This article is an appreciation, on the occasion of his retirement, of some of the most lovely concepts and results that Alan has contributed to the field.Comment: This article will appear, in slightly different form, in the Complexity Theory Column of the September 2014 issue of SIGACT New

Logic Column 14: Nominal Logic and Abstract Syntax

Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding correctly. We present an approach called nominal abstract syntax that has attracted considerable interest since its introduction approximately six years ago. After an overview of other approaches, we describe nominal abstract syntax and nominal logic, a logic for reasoning about nominal abstract syntax. We also discuss applications of nominal techniques to programming, automated reasoning, and identify some future directions.Comment: 24 page

Logic Column 19: Symbolic Model Checking for Temporal-Epistemic Logics

This article surveys some of the recent work in verification of temporal epistemic logic via symbolic model checking, focusing on OBDD-based and SAT-based approaches for epistemic logics built on discrete and real-time branching time temporal logics.Comment: 23 page

A Quick Glance at Quantum Cryptography

The recent application of the principles of quantum mechanics to cryptography has led to a remarkable new dimension in secret communication. As a result of these new developments, it is now possible to construct cryptographic communication systems which detect unauthorized eavesdropping should it occur, and which give a guarantee of no eavesdropping should it not occur. CONTENTS P3. Cryptographic systems before quantum cryptography P7. Preamble to quantum cryptography P10. The BB84 quantum cryptographic protocol without noise P16. The BB84 quantum cryptographic protocol with noise P19..The B92 quantum cryptographic protocol P21. EPR quantum cryptographic protocols P25. Other protocols P25. Eavesdropping stategies and counter measures P26. Conclusion P29. Appendix A. The no cloning theorem P30. Appendix B. Proof that an undetectable eavesdropper can obtain no information from the B92 protocol P31. Appendix C. Part of a Rosetta stone for quantum mechanics P44. ReferencesComment: 54 pages, LaTeX with 6 figures as well as 3 graphics files embedded as text on pages 40 and 41. To appear in Cryptologia. Document also found at http://www.csee.umbc.edu/~lomonaco . In this version, problems with figures have been correcte

Reachability is in DynFO

Patnaik and Immerman introduced the dynamic complexity class DynFO of database queries that can be maintained by first-order dynamic programs with the help of auxiliary relations under insertions and deletions of edges (Patnaik and Immerman 1997). This article confirms their conjecture that the Reachability query is in DynFO. As a byproduct it is shown that the rank of a matrix with small values can be maintained in DynFO(+,x). It is further shown that the (size of the) maximum matching of a graph can be maintained in non-uniform DynFO, another extension of DynFO, with non-uniform initialisation of the auxiliary relations

The GHZ state in secret sharing and entanglement simulation

In this note, we study some properties of the GHZ state. First, we present a quantum secret sharing scheme in which the participants require only classical channels in order to reconstruct the secret; our protocol is significantly more efficient than the trivial usage of teleportation. Second, we show that the classical simulation of an n-party GHZ state requires at least n log n - 2n bits of communication. Finally, we present a problem simpler than the complete simulation of the multi-party GHZ state, that could lead to a no-go theorem for GHZ state simulation.Comment: 5 page

The Complexity of Reasoning for Fragments of Autoepistemic Logic

Autoepistemic logic extends propositional logic by the modal operator L. A formula that is preceded by an L is said to be "believed". The logic was introduced by Moore 1985 for modeling an ideally rational agent's behavior and reasoning about his own beliefs. In this paper we analyze all Boolean fragments of autoepistemic logic with respect to the computational complexity of the three most common decision problems expansion existence, brave reasoning and cautious reasoning. As a second contribution we classify the computational complexity of counting the number of stable expansions of a given knowledge base. To the best of our knowledge this is the first paper analyzing the counting problem for autoepistemic logic

A Survey on Operational State Complexity

Descriptional complexity is the study of the conciseness of the various models representing formal languages. The state complexity of a regular language is the size, measured by the number of states of the smallest, either deterministic or nondeterministic, finite automaton that recognises it. Operational state complexity is the study of the state complexity of operations over languages. In this survey, we review the state complexities of individual regularity preserving language operations on regular and some subregular languages. Then we revisit the state complexities of the combination of individual operations. We also review methods of estimation and approximation of state complexity of more complex combined operations

A Call to Arms: Revisiting Database Design

Good database design is crucial to obtain a sound, consistent database, and - in turn - good database design methodologies are the best way to achieve the right design. These methodologies are taught to most Computer Science undergraduates, as part of any Introduction to Database class. They can be considered part of the "canon", and indeed, the overall approach to database design has been unchanged for years. Moreover, none of the major database research assessments identify database design as a strategic research direction. Should we conclude that database design is a solved problem? Our thesis is that database design remains a critical unsolved problem. Hence, it should be the subject of more research. Our starting point is the observation that traditional database design is not used in practice - and if it were used it would result in designs that are not well adapted to current environments. In short, database design has failed to keep up with the times. In this paper, we put forth arguments to support our viewpoint, analyze the root causes of this situation and suggest some avenues of research.Comment: Removed spurious column break. Nothing else was change

Quantum Algorithms

This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a summary of the early quantum algorithms, a description of the Abelian Hidden Subgroup algorithms (including Shor's factoring and discrete logarithm algorithms), quantum searching and amplitude amplification, quantum algorithms for simulating quantum mechanical systems, several non-trivial generalizations of the Abelian Hidden Subgroup Problem (and related techniques), the quantum walk paradigm for quantum algorithms, the paradigm of adiabatic algorithms, a family of ``topological'' algorithms, and algorithms for quantum tasks which cannot be done by a classical computer, followed by a discussion.Comment: 71 pages, 1 figure, to appear in the Springer Encyclopedia of Complexity and Systems Scienc