The ISO standard for the Standard Generalized Markup Language (SGML) provides a syntactic meta-language for the definition of textual markup systems. In the standard, the right-hand sides of productions are based on regular expressions, although only regular expressions that denote words unambiguously, in the sense of the ISO standard, are allowed. In general, a word that is denoted by a regular expression is witnessed by a sequence of occurrences of symbols in the regular expression that match the word. In an unambiguous regular expression as defined by Book, Even, Greibach, and Ott, each word has at most one witness. But the SGML standard also requires that a witness be computed incrementally from the word with a one-symbol lookahead; we call such regular expressions 1-unambiguous. A regular language is a 1-unambiguous language if it is denoted by some 1-unambiguous regular expression. We give a Kleene theorem for 1-unambiguous languages and characterize 1-unambiguous regu...

To build survivable information systems (i.e., systems that continue to provide their services in spite of coordinated attacks), it is necessary to detect and isolate intrusions before they impact system performance or functionality. Previous research in this area has focussed primarily on detecting intrusions after the fact, rather than preventing them in the first place. We have developed a new approach based on specifying intended program behaviors using patterns over sequences of system calls. The patterns can also capture conditions on the values of system-call arguments. At runtime, we intercept the system calls made by processes, compare them against specifications, and disallow (or otherwise modify) those calls that deviate from specifications. Since our approach is capable of modifying a system call before it is delivered to the operating system kernel, it is capable of reacting before any damage-causing system call is executed by a process under attack. We present our specification language and illustrate its use by developing a specification for the ftp server. Observe that in our approach, every system call is intercepted and subject to potentially expensive operations for matching against many patterns that specify normal/abnormal behavior. Thus, minimizing the overheads incurred for pattern-matching is critical for the viability of our approach. We solve this problem by developing a new, low-overhead algorithm for matching runtime behaviors against specifications. A salient feature of our algorithm is that its runtime is almost independent of the number of patterns. In most cases, it uses a constant amount of time per system call intercepted, and uses a constant amount of storage, both independent of either the size or number of patterns. These benefits m...

In this paper we define timed regular expressions, an extension of regular expressions for specifying sets of densetime discrete-valued signals. We show that this formalism is equivalent in expressive power to the timed automata of Alur and Dill by providing a translation procedure from expressions to automata and vice versa. The result is extended to !-regular expressions (B uchi's theorem). 1. Introduction Timed automata, i.e. automata equipped with clocks [AD94], have been studied extensively in recent years as they provide a rigorous model for reasoning about the quantitative temporal aspects of systems. Together with realtime logics and process algebras they constitute the underlying theoretical basis for the specification and verification of real-time systems. Kleene's theorem [K56], stating that the regular (or rational) subsets of \Sigma are exactly the recognizable ones (those accepted by finite automata), is one of the cornerstones of automata theory. No such theorem has ...

. We introduce a notion of a partial derivative of a regular expression. It is a generalization to the non-deterministic case of the known notion of a derivative invented by Brzozowski. We give a constructive definition of partial derivatives, study their properties, and employ them to develop a new algorithm for turning regular expressions into relatively small NFA and to provide certain improvements to Brzozowski's algorithm constructing DFA. We report on a prototype implementation of our algorithm constructing NFA and present some examples. Introduction In 1964 Janusz Brzozowski introduced word derivatives of regular expressions and suggested an elegant algorithm turning a regular expression r into a deterministic finite automata (DFA); the main point of the algorithm is that the word derivatives of r serve as states of the resulting DFA [5]. In the following years derivatives were recognized as a quite useful and productive tool. Conway [8] uses derivatives to present various comp...

Theoretical computer science treats any computational subject for which a good model can be created. Research on formal models of computation was initiated in the 1930s and 1940s by Turing, Post, Kleene, Church, and others. In the 1950s and 1960s programming languages, language translators, and operating systems were under development and therefore became both the subject and basis for a great deal of theoretical work. The power of computers of this period was limited by slow processors and small amounts of memory, and thus theories (models, algorithms, and analysis) were developed to explore the efficient use of computers as well as the inherent complexity of problems. The former subject is known today as algorithms and data structures, the latter computational complexity. The focus of theoretical computer scientists in the 1960s on languages is reflected in the first textbook on the subject, Formal Languages and Their Relation to Automata by John Hopcroft and Jeffrey Ullman. This influential book led to the creation of many languagecentered theoretical computer science courses; many introductory theory courses today continue to reflect the content of this book and the interests of theoreticians of the 1960s and early 1970s. Although

In this paper we define timed regular expressions, a formalism for specifying discrete behaviors augmented with timing information, and prove that its expressive power is equivalent to the timed automata of Alur and Dill. This result is the timed analogue of Kleene Theorem and, similarly to that result, the hard part in the proof is the translation from automata to expressions. This result is extended from finite to infinite (in the sense of B uchi) behaviors. In addition to these fundamental results, we give a clean algebraic framework for two commonly-accepted formalism for timed behaviors, time-event sequences and piecewise-constant signals. 1

We present a new approach that enables compiler optimization of procedure calls and loop nests containing procedure calls. We introduce two interprocedural transformations that move loops across procedure boundaries, exposing them to traditional optimizations on loop nests. These transformations are incorporated into a code generation algorithm for a shared-memory multiprocessor. The code generator relies on a machine model to estimate the expected benefits of loop parallelization and parallelism-enhancing transformations. Several transformation strategies are explored and one that minimizes total execution time is selected. Efficient support of this strategy is provided by an existing interprocedural compilation system. We demonstrate the potential of these techniques by applying this code generation strategy to two scientific applications programs.

To my parents and uncle Frank

. The Standard Generalized Markup Language (SGML), an ISO standard, has become the accepted method of defining markup conventions for text files. SGML is a metalanguage for defining grammars for textual markup in much the same way that Backus--Naur Form is a metalanguage for defining programming-language grammars. Indeed, HTML, the method of marking up a hypertext documents for the World Wide Web, is an SGML grammar. The underlying assumptions of the SGML initiative are that a logical structure of a document can be identified and that it can be indicated by the insertion of labeled matching brackets (start and end tags). Moreover, it is assumed that the nesting relationships of these tags can be described with an extended context-free grammar (the right-hand sides of productions are regular expressions). In this survey of some of the issues raised by the SGML initiative, I reexamine the underlying assumptions and address some of the theoretical questions that SGML raises....

Relational database systems and most objectoriented database systems provide support for queries. Usually these queries represent retrievals over sets or multisets. Many new applications for databases, such as multimedia systems and digital libraries, need support for queries on complex bulk types such as lists and trees. In this paper we describe an object-oriented query algebra for lists and trees. The operators in the algebra preserve the ordering between the elements of a list or tree, even when the result list or tree contains an arbitrary set of nodes from the original tree. We also present predicate languages for lists and trees which allow order-sensitive queries because they use pattern matching to examine groups of list or tree nodes rather than individual nodes. The ability to decompose predicate patterns enables optimizations that make use of indices.