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SUCCINCTNESS OF THE COMPLEMENT AND INTERSECTION OF REGULAR EXPRESSIONS
, 2008
"... 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 ..."
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Cited by 17 (5 self)
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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 worstcase 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 byproduct, 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 fourletter alphabet. When the given regular expressions are oneunambiguous, 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 singleoccurrence regular expressions, we prove a tight exponential lower bound for intersection.
Generating optimal monitors for extended regular expressions
 In Proc. of the 3rd Workshop on Runtime Verification (RV’03), volume 89 of ENTCS
, 2003
"... Ordinary software engineers and programmers can easily understand regular patterns, as shown by the immense interest in and the success of scripting languages like Perl, based essentially on regular expression pattern matching. We believe that regular expressions provide an elegant and powerful spec ..."
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Cited by 17 (7 self)
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Ordinary software engineers and programmers can easily understand regular patterns, as shown by the immense interest in and the success of scripting languages like Perl, based essentially on regular expression pattern matching. We believe that regular expressions provide an elegant and powerful specification language also for monitoring requirements, because an execution trace of a program is in fact a string of states. Extended regular expressions (EREs) add complementation to regular expressions, which brings additional benefits by allowing one to specify patterns that must not occur during an execution. Complementation gives one the power to express patterns on strings more compactly. In this paper we present a technique to generate optimal monitors from EREs. Our monitors are deterministic finite automata (DFA) and our novel contribution is to generate them using a modern coalgebraic technique called coinduction. Based on experiments with our implementation, which can be publicly tested and used over the web, we believe that our technique is more efficient than the simplistic method based on complementation of automata which can quickly lead to a highlyexponential state explosion.
Checking and correcting behaviors of java programs at runtime with javamop
 Electr. Notes Theor. Comput. Sci
, 2005
"... Monitoringoriented programming (MOP) is a software development and analysis technique in which monitoring plays a fundamental role. MOP users can add their favorite or domainspecific requirements specification formalisms into the framework by means of logic plugins, which essentially comprise mon ..."
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Cited by 12 (3 self)
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Monitoringoriented programming (MOP) is a software development and analysis technique in which monitoring plays a fundamental role. MOP users can add their favorite or domainspecific requirements specification formalisms into the framework by means of logic plugins, which essentially comprise monitor synthesis algorithms for properties expressed as formulae. The properties are specified together with declarations stating where and how to automatically integrate the corresponding monitor into the system, as well as what to do if the property is violated or validated. In this paper we present JavaMOP, an MOP environment for developing robust Java applications. Based upon a carefully designed specification schema and upon several logic plugins, JavaMOP allows users to specify and monitor properties which can refer not only to the current program state, but also to the entire execution trace of a program, including past and future behaviors. 1
Generating Optimal Linear Temporal Logic Monitors by Coinduction
 Proceedings of 8th Asian Computing Science Conference (ASIAN’03), volume 2896 of Lecture Notes in Computer Science
, 2004
"... A coinductionbased technique to generate an optimal monitor from a Linear Temporal Logic (LTL) formula is presented in this paper. Such a monitor receives a sequence of states (one at a time) from a running process, checks them against a requirements specification expressed as an LTL formula, a ..."
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Cited by 4 (2 self)
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A coinductionbased technique to generate an optimal monitor from a Linear Temporal Logic (LTL) formula is presented in this paper. Such a monitor receives a sequence of states (one at a time) from a running process, checks them against a requirements specification expressed as an LTL formula, and determines whether the formula has been violated or validated. It can also say whether the LTL formula is not monitorable any longer, i.e., that the formula can in the future neither be violated nor be validated. A Web interface for the presented algorithm adapted to extended regular expressions is available.
An Effective Algorithm for The Membership Problem for Extended Regular Expressions
"... Abstract. By adding the complement operator (¬), extended regular expressions (ERE) can encode regular languages nonelementarily more succinctly than regular expressions. The ERE membership problem asks whether a word w of size n belongs to the language of an ERE R of size m. Unfortunately, the bes ..."
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Abstract. By adding the complement operator (¬), extended regular expressions (ERE) can encode regular languages nonelementarily more succinctly than regular expressions. The ERE membership problem asks whether a word w of size n belongs to the language of an ERE R of size m. Unfortunately, the best known membership algorithms are either nonelementary in m or otherwise require space Ω(n 2)andtimeΩ(n 3); since in many practical applications n can be very large (in the order of billions, e.g., in testing where w represents the execution trace of some system), these space and time requirements could be prohibitive. In this paper we present a simple to implement ERE membership algorithm that runs in space O(n·(m+logn)·2 m ·k) andintimeO(n 2 ·(m+logn) 2 ·2 m ·k), where k is the number of complement operators in R. The presented algorithm outperforms the best known algorithms when n is large. Topics. Automata and formal languages, algorithms, datastructures. 1
www.stacsconf.org SUCCINCTNESS OF THE COMPLEMENT AND INTERSECTION OF REGULAR EXPRESSIONS
, 2008
"... Abstract. 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 ..."
Abstract
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Abstract. 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 worstcase 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 byproduct, 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 fourletter alphabet. When the given regular expressions are oneunambiguous, 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 singleoccurrence regular expressions, we prove a tight exponential lower bound for intersection. 1.