Neil Immerman

Nondeterministic space is closed under complementation

In this paper we show that nondeterministic space

Languages that capture complexity classes

s(n)

Efficient pattern matching over event streams

is closed under complementation for

An optimal lower bound on the number of variables for graph identification

s(n)

Describing Graphs: A First-Order Approach to Graph Canonization

greater than or equal to

Number of quantifiers is better than number of tape cells

\log n

Expressibility and parallel complexity

. It immediately follows that the context-sensitive languages are closed under complementation, thus settling a question raised by Kuroda [Inform. and Control, 7 (1964), pp. 207–233].

Sparse sets in NP-P: EXPTIME versus NEXPTIME*

We present a series of operators of apparently increasing power which when added to first-order logic produce a series of languages in which exactly the properties checkable in a certain complexity class may be expressed. We thus give alternate characterizations of most important complexity classes. We also introduce reductions appropriate for our setting: first-order translations, and a restricted, quantifier free version of these called projection translations. We show that projection translations are a uniform version of Valiant’s projections, and that the usual complete problems remain complete via these very restrictive reductions.

On Supporting Kleene Closure over Event Streams

Pattern matching over event streams is increasingly being employed in many areas including financial services, RFIDbased inventory management, click stream analysis, and electronic health systems. While regular expression matching is well studied, pattern matching over streams presents two new challenges: Languages for pattern matching over streams are significantly richer than languages for regular expression matching. Furthermore, efficient evaluation of these pattern queries over streams requires new algorithms and optimizations: the conventional wisdom for stream query processing (i.e., using selection-join-aggregation) is inadequate. In this paper, we present a formal evaluation model that offers precise semantics for this new class of queries and a query evaluation framework permitting optimizations in a principled way. We further analyze the runtime complexity of query evaluation using this model and develop a suite of techniques that improve runtime efficiency by exploiting sharing in storage and processing. Our experimental results provide insights into the various factors on runtime performance and demonstrate the significant performance gains of our sharing techniques.

The Boundary Between Decidability and Undecidability for Transitive-Closure Logics

In this paper we show that Ω(n) variables are needed for first-order logic with counting to identify graphs onn vertices. Thek-variable language with counting is equivalent to the (k−1)-dimensional Weisfeiler-Lehman method. We thus settle a long-standing open problem. Previously it was an open question whether or not 4 variables suffice. Our lower bound remains true over a set of graphs of color class size 4. This contrasts sharply with the fact that 3 variables suffice to identify all graphs of color class size 3, and 2 variables suffice to identify almost all graphs. Our lower bound is optimal up to multiplication by a constant becausen variables obviously suffice to identify graphs onn vertices.