. This paper addresses the problem of building a Boolean dataflow network (sequential circuit) recognizing the language described by a regular expression. The main result is that both the construction time and the size of the resulting network are linear with respect to the size of the regular expression. Introduction "Grep" machine: Let \Sigma be a vocabulary, L be a regular language on \Sigma . A "grep" machine is a machine receiving a sequence s 0 ; s 1 ; : : : ; s n ; : : : of symbols (s i 2 \Sigma ) and computing a sequence b 0 ; b 1 ; : : : ; b n ; : : : of Booleans, such that b n is true if and only if the word s 0 s 1 : : : s n belongs to L 2 . This paper addresses the problem of building a "grep" machine for languages described by regular expressions. This problem is rather classical [4, 11, 10, 3, 1, 2]. We propose a solution which, to our knowledge, is new: Informally, it consists of building, from a regular expression E, a "circuit" (or Boolean data-flow network) explori...

In this paper we show that minimum-cost spanning tree is a special case of the closed semiring path-finding problem. This observation gives us a non-recursive algorithm for finding minimumcost spanning trees on mesh-connected computers that has the same asymptotic running time but is much simpler than the previous recursive algorithms.

Let E be a regular expression. Our aim is to establish a theoretical relation between two well-known automata recognizing the language of E, namely the position automaton PE constructed by Glushkov or McNaughton and Yamada, and the equation automaton EE constructed by Mirkin or Antimirov. We define the notion of c-derivative (for canonical derivative) of a regular expression E and show that if E is linear then two Brzozowski’s derivatives of E are aci-similar if and only if the corresponding c-derivatives are identical. It allows us to represent the Berry-Sethi’s set of continuations of a position by a unique c-derivative, called the c-continuation of the position. Hence the definition of CE, the c-continuation automaton of E, whose states are pairs made of a position of E and of the associated c-continuation. If states are viewed as positions, CE is isomorphic to PE. On the other hand, a partial derivative, as defined by Antimirov, is a class of c-derivatives for some equivalence relation, thus CE reduces to EE. Finally CE makes it possible to go from PE to EE, while this cannot be achieved directly (from the state graphs). These theoretical results lead to an O(|E | 2) space and time algorithm to compute the equation automaton, where |E | is the size of the expression. This is the complexity of the most efficient constructions yielding the position automaton, while the size of the equation automaton is not greater and generally much smaller than the size of the position automaton.

Reliance on networked information systems to support critical infrastructures prompts interest in making network information systems survivable, so that they continue functioning even when under attack. To build survivable systems, attacks must be detected and reacted to before they impact performance or functionality. Previous survivable systems research focussed primarily on detecting intrusions, rather than on preventing or containing damage due to intrusions. We have therefore developed a new approach that combines early attack detection with automated reaction for damage prevention and containment, as well as tracing and isolation of attack origination point(s). Our approach is based on specifying security-relevant behaviors using patterns over sequences of observable events, such as a process’s system calls and their arguments, and the contents of network packets. By intercepting actual events at runtime and comparing them to specifications, attacks can be detected and operations associated with the deviant events can be modified to thwart the attack. Being based on security-relevant behaviors rather than known attack signatures, our approach can protect against unknown attacks. At the same time, our approach produces few false positives – a property that is critical for automating reactions. Our host-based mechanisms for attack detection and isolation coordinate with network routers enhanced with active networking technology in order to trace the origin of the attack and isolate the attacker. 1

In this paper, we describe the design, architecture, and the lessons learned from the implementation of a fast regular expression indexing engine FREE. FREE uses a prebuilt index to identify the text data units which may contain a matching string and only examines these further. In this way, FREE shows orders of magnitude performance improvement in certain cases over standard regular expression matching systems, such as lex, awk and grep [18, 4].

This paper presents a taxonomy of finite automata construction algorithms. Each algorithm is classified into one of two families: those based upon the structure of regular expressions, and those based upon the automata-theoretic work of Myhill and Nerode. Many of the algorithms appearing in the literature are based upon the structure of regular expressions. In this paper, we make this term precise by defining regular expressions as a \Sigma-term algebra, and automata constructions as various \Sigma-algebras of automata. Each construction algorithm is then presented as the unique natural homomorphism from the \Sigmaterm algebra of regular expressions to the appropriate \Sigma-algebra of automata. The concept of duality is introduced and used to derive more practical construction algorithms. In this way, we successfully present (and relate) algorithms given by Thompson, Berry and Sethi, McNaughton and Yamada, Glushkov, and Aho, Sethi, and Ullman. Efficient implementations (including thos...

The Standard Generalized Markup Language (SGML) is an ISO standard that provides a syntactic meta-language for the definition of textual markup systems, which are used to indicate the structure of documents so that they can be electronically typeset, searched, and communicated. We address only one problem raised by the standard, namely: In SGML, the right-hand sides of context-free productions are regular expressions, called content models, that are restricted to be what the standard calls "unambiguous," but what is more appropriately called deterministic. We solve the problem of how to define determinism precisely, how to recognize deterministic regular expressions efficiently, and how to recognize deterministic regular languages. Any SGML parser must check that a given document grammar conforms to the standard; that is, it must validate it. Hence, our results are an important step in the clarification of the standard and in the efficient implementation of an SGML parser fo...

We study the succinctness of the complement and intersection of regular expressions. In particular, we show that when constructing a regular expression defining the complement of a given regular expression, a double exponential size increase cannot be avoided. Similarly, when constructing a regular expression defining the intersection of a fixed and an arbitrary number of regular expressions, an exponential and double exponential size increase, respectively, can in worst-case not be avoided. All mentioned lower bounds improve the existing ones by one exponential and are tight in the sense that the target expression can be constructed in the corresponding time class, i.e., exponential or double exponential time. As a by-product, we generalize a theorem by Ehrenfeucht and Zeiger stating that there is a class of DFAs which are exponentially more succinct than regular expressions, to a fixed four-letter alphabet. When the given regular expressions are one-unambiguous, as for instance required by the XML Schema specification, the complement can be computed in polynomial time whereas the bounds concerning intersection continue to hold. For the subclass of single-occurrence regular expressions, we prove a tight exponential lower bound for intersection.

Feature interactions in telecommunications is an active research area. Many approaches to solve the so-called feature interaction problem have been proposed. However, all these approaches consider feature interaction as a somewhat isolated problem, in particular it is not seen in the context of evolving legacy systems and third party features in a deregulated market environment. An exception is the approach by Marples and Magill [MM98, Mar00], which presents an interaction detection mechanism and an essentially manual resolution approach. We develop an automatic resolution approach that can be integrated with Marples and Magill’s detection mechanism. We distinguish two key concepts, namely solutions and resolutions. The former are essentially possible behaviours of the system, they are not qualified as desirable or undesirable, the latter are the desirable solutions. Our approach allows for automatic removal of undesired behaviour and selection of the “best ” desired behaviour. The correctness, complexity and suitability of our approach are analysed. Two case studies support these more theoretical considerations. Our approach is transferable to other areas, such as quality of service management, and is not restricted to network architectures with a single point of control.

Abstract. We consider the use of state elimination to construct shorter regular expressions from finite-state automata. Although state elimination is an intuitive method for computing regular expressions from finitestate automata, the resulting regular expressions are often very long and complicated. We examine the minimization of finite-state automata to obtain shorter expressions first. Then, we introduce vertical chopping based on bridge states and horizontal chopping based on the structural properties of given finite-state automata. We prove that we should not eliminate bridge states until we eliminate all non-bridge states to obtain shorter regular expressions. In addition, we suggest heuristics for state elimination that lead to shorter regular expressions based on vertical chopping and horizontal chopping. Note that we have omitted almost all proofs in this preliminary version. 1