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By Christos H. Papadimitriou (auth.), Fernando Orejas, Paul G. Spirakis, Jan van Leeuwen (eds.)

This booklet constitutes the refereed court cases of the twenty eighth foreign Colloquium on Automata, Languages and Programming, ICALP 2001, held in Crete, Greece in July 2001.
The eighty revised papers awarded including keynote contributions and 4 invited papers have been conscientiously reviewed and chosen from a complete of 208 submissions. The papers are equipped in topical sections on algebraic and circuit complexity, set of rules research, approximation and optimization, complexity, concurrency, effective information constructions, graph algorithms, language concept, codes and automata, version checking and protocol research, networks and routing, reasoning and verification, scheduling, safe computation, specification and deduction, and structural complexity.

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Extra resources for Automata, Languages and Programming: 28th International Colloquium, ICALP 2001 Crete, Greece, July 8–12, 2001 Proceedings

Example text

In these models, configurations are vectors of words, and transition relations between configurations are defined by means of sets of rewriting rules. 1 Rewriting Systems Let Σ be a finite alphabet (set of symbols). For n ≥ 1, an n-dim rewriting rule r over Σ is a pair x, y where x, y ∈ (Σ ∗ )n . We denote such a rule by r : x → y. The left hand side (resp. right hand side) of r, denoted by lhs(r) (resp. rhs(r)), is the vector x (resp. y). A n-dim rewriting system is a finite set of n-dim rewriting rules.

M − 1}, qi = qi+1 , and (3) qm = q1 . Boigelot et al. have shown the following result: Theorem 2 ([BGWW97]). Let R be a 1-dim control loop. Then, for every effectively recognizable set φ, the set Rc∗ (φ) is effectively recognizable. For systems of higher dimensions (even for 2-dim systems), the Rc∗ image is not recognizable, in general. Indeed, consider for instance the self-loop R = {(q, , ) → (q, a, a)}. Then, Rc∗ (q, , ) = {(q, an , an ) : n ≥ 0} which is a non-recognizable set. [BGWW97] provides a characterization of the control loops R such that Rc∗ preserves recognizability, as well as an algorithm which constructs for such loops a finite automaton representing the Rc∗ image of any given recognizable set.

N}. aj = bij . We consider the product generalization of this relation to vectors of words. Let R be a n-dim rewriting system over Σ. We define the weak cyclic rewriting relation Rwc ∈ (Σ ∗ )n × (Σ ∗ )n ) as follows: for every u, v ∈ (Σ ∗ )n , (u, v) ∈ Rwc if u, v ∈ Rc (u ), and v v . t. the subword relation if ∀u, v ∈ (Σ ∗ )n , if v ∈ L and u v, then u ∈ L. , the smallest downward closed set which includes L. Clearly, for every ∗ (φ) is downward closed. t is a recognizable set, the following fact can be deduced.

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