Relations between Semantics and Complexity of Recursive Programs

has been devoted to a single subject (complexity theory), this Volume B is more diverse. Roughly, we can distinguish the following areas: formal languages and rewriting (Chapters 1−6), programming (7−10), semantics (11−13), logics (14−16), databases (17), and concurrency (18−19). The chapters in this volume are: 1. Finite Automata (D. Perrin, pp. 1−57) is a survey of regular languages: an algebraic introduction, syntactic monoids, regular expressions, ambiguity, star-height, finite power property, Kleene's theorem and pumping lemma. Then a few topics are treated in more depth: some subregular language families (star-free, aperiodic, locally testable, piecewise testable languages), automata for pattern matching, recognizable sets of numbers, random access automata, and Schü tzenberger's Theorem. 2. Context-Free Languages (J. Berstel & L. Boasson, pp. 59−102) also presents some less traditional results: viz. the Hotz group, several pumping lemmas, interchange lemma and square-free words, and degenerated iterative pairs. The second half of this paper is devoted to nongenerators of the family of context-free languages, and to context-free groups. Nongenerators are considered with respect to rational cones (algebras of which the carrier set is a language family and the operations are finite-state transductions). A finitely generated group is context-free if the language of all words equivalent to the unit is context-free. Global and local characterizations of these groups are given. a proof of Ehrenfeucht's conjecture. The second part is devoted to the relation between languages and formal power series in noncommuting variables. Regular languages can be characterized in terms of certain rational power series as context-free languages can by some algebraic power series. In this context (un)decidability results, the commutative case, and ambiguity are discussed. 4. Automata on Infinite Objects (W. Thomas, pp. 133−191) deals with finite-state accep-tors operating on infinite words or trees. In part I ω-regular languages are characterized algebraically, logically, and by automata. Closure under Boolean operations and topological issues are treated as well. Special topics, like star-free ω-languages, their relation with propositional linear-time logic, and context-free ω-languages conclude this part. Part II is devoted to finite top-down automata for rooted node-labeled infinite trees, characterizations of the corresponding families of tree languages, decidability of the emptiness problem, the relation to logics and to regular infinite games. 5. Graph Rewriting: An Algebraic and Logic Approach (B. Courcelle, pp. 193−242) uses logics, universal algebra, and category theory to describe properties of (hyper)graphs. Context-free sets of hypergraphs are defined by hyperedge-replacement grammars or as a solution of …