15984778
XML transformation by tree-walking transducers with invisible pebbles
The pebble tree automaton and the pebble tree transducer are enhanced by additionally allowing an unbounded number of "invisible" pebbles (as opposed to the usual ("visible" ones). The resulting pebble tree automata recognize the regular tree languages (i.e., can validate all generalized DTD's) and hence can find all matches of MSO definable n-ary patterns. Moreover, when viewed as a navigational device, they lead to an XPath-like formalism that has a path expression for every MSO definable binary pattern. The resulting pebbletree transducers can apply arbitrary MSO definable tests to (the observable part of) their configurations, they (still) have a decidable typechecking problem, and they can model the recursion mechanism of XSLT. The time complexity ofthe typechecking problem for conjunctive queries that use MSO definable binary patterns can often be reduced through the use of invisible pebbles.
17560850
Clique-Width for Four-Vertex Forbidden Subgraphs
Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms. The notion of clique-width extends the one of treewidth, since bounded treewidth implies bounded clique-width. We give a complete classification of all graph classes defined by forbidden induced subgraphs of at most four vertices with respect to bounded or unbounded clique-width.
27165586
A new natural structural congruence in the pi-calculus with replication
Abstract.In the $\pi$-calculus with replication, a new structural congruence called “middle” congruence is investigated: a notion of structural equivalence of processes in which replication of a process is viewed as a potential rather than an actual infinite number of copies of the process, in the sense that copies are spawned at need rather than produced all at once. It is slightly weaker than standard congruence (which is also of the potential type) but stronger than the extended congruence investigated before by the authors (which is of the actual type). It is shown that middle congruence has the same desirable properties as extended congruence: it is decidable and it has a concrete multiset semantics. Thus, these properties do not depend on the distinction between potential and actual replication.
5981521
Nested Pebbles and Transitive Closure
First-order logic with k-ary deterministic transitive closure has the same power as two-way k-head deterministic automata that use a finite set of nested pebbles. This result is valid for strings, ranked trees, and in general for families of graphs having a fixed automaton that can be used to traverse the nodes of each of the graphs in the family. Other examples of such families are grids, toruses, and rectangular mazes.
17757601
A Kleene characterization of computability
The recursively enumerable binary relations are the smallest class containing all singleton relations and closed under union, concatenation, Kleene star, composition, and transitive closure.
20050455
Clique-Width for 4-Vertex Forbidden Subgraphs
Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms. The notion of clique-width extends the one of treewidth, since bounded treewidth implies bounded clique-width. We give a complete classification of all graph classes defined by forbidden induced subgraphs of at most four vertices with respect to bounded or unbounded clique-width.
5775307
Compositional Verification of Multi-Agent Systems in Temporal Multi-Epistemic Logic
Compositional verification aims at managing the complexity of the verification process by exploiting compositionality of the system architecture. In this paper we explore the use of a temporal epistemic logic to formalize the process of verification of compositional multi-agent systems. The specification of a system, its properties and their proofs are of a compositional nature, and are formalized within a compositional temporal logic: Temporal Multi-Epistemic Logic. It is shown that compositional proofs are valid under certain conditions. Finally, the possibility of incorporating default persistence of information in a system, is explored.
13469765
Decidability of the Finiteness of Ranges of Tree Transductions
Abstract The finiteness of ranges of tree transductions is shown to be decidable for TBY + , the composition closure of macro tree transductions. Furthermore, TBY + definable sets and TBY + computable relations are considered, which are obtained by viewing a tree as an expression that denotes an element of a given algebra. A sufficient condition on the considered algebra is formulated under which the finiteness problem is decidable for TBY + definable sets and for the ranges of TBY + computable relations. The obtained result applies in particular to the class of string languages that can be defined by TBY + transductions via the yield mapping. This is a large class which is proved to form a substitution-closed full AFL.
17739753
Finite Languages for the Representation of Finite Graphs
We introduce a new way of specifying graphs: through languages, i.e., sets of strings. The strings of a given (finite, prefix-free) language represent the vertices of the graph; whether or not there is an edge between the vertices represented by two strings is determined by the pair of symbols at the first position in these strings where they differ. With this new, “positional” or lexicographic, method, classical and well-understood ways of specifying languages can now be used to specify graphs, in a compact way; thus, (small) finite automata can be used to specify (large) graphs. Since (prefix-free) languages can be viewed as trees, our method generalizes the hierarchical specification of particular types of graphs such as cographs and VSP graphs. Our main results demonstrate an intrinsic relationship between the fundamental operations of language concatenation and graph substitution.
11417476
Look-Ahead on Pushdowns
Abstract The general notion of look-ahead on pushdowns is used to prove that (1) the deterministic iterated pushdown languages are closed under complementation, (2) the deterministic iterated pushdown languages are properly included in the non-deterministic iterated pushdown languages; the counter example is a very simple linear context-free language, independent of the amount of iteration, (3) LL ( k ) iterated indexed grammars can be parsed by deterministic iterated pushdown automata, and (4) it is decidable whether an iterated indexed grammar is LL ( k ). Analogous results hold for iterated pushdown automata with regular look-ahead on the input, and LL -regular iterated indexed grammars.
9307461
Context Free Normal Systems and ETOL Systems
Abstract The relationship between extended context free normal systems (a nondeterministic version of Tag systems of Post with deletion number equal to 1 and using nonterminals) and ETOL systems is considered. It is demonstrated that the class of languages generated by context free normal systems (denoted L (ECFN)) lies strictly between the clas of EOL languages (denoted L (EOL)) and the class of ETOL languages. Several characterizations of L (ECFN)) in terms of L (EOL)) are provided and a number of closure properties of L '(ECFN) are established.