A general method that represents the state space symbolically instead of explicitly is described. The generality of the method comes from using a dialect of the mu-calculus as the primary specification language. A model-checking algorithm for mu-calculus formulas which uses R.E. Bryant's (1986) binary decision diagrams to represent relations and formulas symbolically is described. It is then shown how the novel mu-calculus model checking algorithm can be used to derive efficient decision procedures for CTL model checking, satisfiability of linear-time temporal logic formulas, strong and weak observational equivalence of finite transition systems, and language containment of finite omega -automata. This eliminates the need to describe complicated graph-traversal or nested fixed-point computations for each decision procedure. The authors illustrate the practicality of their approach to symbolic model checking by discussing how it can be used to verify a simple synchronous pipeline. >

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Symbolic model checking: 10/sup 20/ states and beyond

The Department of Languages provides a vital component in the undergraduate liberal arts education offered at the University of WisconsinEau Claire. The department promotes multilingualism as the key to intercultural understanding. It does so through courses in foreign language, culture, and literature, including English language for native speakers of other languages; major and minor programs in a number of world languages; study abroad opportunities and internships in many countries; and student/faculty collaborative research. Graduates from the Department of Languages serve at home and abroad as ambassadors for a diverse, peacefully interacting global society.

Ω-languages

Features express the variabilities and commonalities among programs in a software product line (SPL). A feature model defines the valid combinations of features, where each combination corresponds to a program in an SPL. SPLs and their feature models evolve over time. We classify the evolution of a feature model via modifications as refactorings, specializations, generalizations, or arbitrary edits. We present an algorithm to reason about feature model edits to help designers determine how the program membership of an SPL has changed. Our algorithm takes two feature models as input (before and after edit versions), where the set of features in both models are not necessarily the same, and it automatically computes the change classification. Our algorithm is able to give examples of added or deleted products and efficiently classifies edits to even large models that have thousands of features.

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Reasoning about edits to feature models

We propose timed automata to model the behavior of real-time systems over time. Our definition provides a simple, and yet powerful, way to annotate state-transition graphs with timing constraints using finitely many real-valued clocks. A timed automaton accepts timed words — strings in which a real-valued time of occurrence is associated with each symbol. We study timed automata from the perspective of formal language theory: we consider closure properties, decision problems, and subclasses. We discuss the application of this theory to automatic verification of real-time requirements of finite-state systems.

The Theory of Timed Automata

Automata on infinite words are used for specification and verification of nonterminating programs. Different types of automata induce different levels of expressive power, of succinctness, and of complexity. Alternating automata have both existential and universal branching modes and are particularly suitable for specification of programs. In a weak alternating automata the state space is partitioned into partially ordered sets, and the automaton can proceed from a certain set only to smaller sets. Reasoning about weak alternating automata is easier than reasoning about alternating automata with no restricted structure. Known translations of alternating automata to weak alternating automata involve determinization, and therefore involve a double-exponential blow-up. In this paper we describe a quadratic translation, which circumvents the need for determinization, of Buchi and co-Buchi alternating automata to weak alternating automata. Beyond the independent interest of such a translation, it gives rise to a simple complementation algorithm for nondeterministic Buchi automata.

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R. P. Kurshan

Papers

A unified approach for showing language inclusion and equivalence between various types of Ω-automata