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.
15175574
Branching synchronization grammars with nested tables
A generalization of ET0L systems is introduced: grammars with branching synchronization and nested tables. The main result is that branching synchronization grammars with tables of nesting depth n have the same string- and tree-generating power as n-fold compositions of top-down tree transducers. Based on this it is shown, e.g., that the family of generated string languages is a full principal AFL for each n.
47462408
The equivalence problem for deterministic MSO tree transducers is decidable
It is decidable for deterministic MSO definable graph-to-string or graph-to-tree transducers whether they are equivalent on a context-free set of graphs.
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.
14472583
An exercise in structural congruence
Milner's structural congruence is decidable for the pi-calculus without restriction, in exponential space.
14239266
The Equivalence Problem for Deterministic MSO Tree Transducers Is Decidable
It is decidable for deterministic MSO definable graph-to-string or graph-to-tree transducers whether they are equivalent on a context-free set of graphs.
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.
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.
495864
Infinitary Default Logic for Specification of Nonmonotonic Reasoning
In this paper we study constructions leading to the formation of belief sets by agents. We focus on the situation when possible belief sets are built incrementally in stages. We call an infinite sequence of theories that represents such a process a reasoning trace. A set of reasoning traces describing all possible reasoning scenarios for the agent is called a reasoning frame. Default logic by Reiter is not powerful enough to represent reasoning frames. In the paper we introduce a generalization of default logic of Reiter by allowing infinite sets of justifications. We call this formalism infinitary default logic. In the main result of the paper we show that every reasoning frame can be represented by an infinitary default theory. A similar representability result for antichains of theories (belief frames) is also presented.
1862248
Monotonicity and Persistence in Preferential Logics
An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be safely added to the premises without destroying any of the consequences: we say they respect monotonicity. Also, there may be formulae that, when they are a consequence, can not be invalidated when adding any formula to the premises: we call them conservative. We study these two classes of formulae for preferential logics, and show that they are closely linked to the formulae whose truth-value is preserved along the (preferential) ordering. We will consider some preferential logics for illustration, and prove syntactic characterization results for them. The results in this paper may improve the efficiency of theorem provers for preferential logics.
11003400
Passes and Paths of Attributive Grammars
An attribute grammar is pure (left-to-right) multi-pass if a bounded number of left-to-right passes over the derivation tree suffice to compute all its attributes. There is no requirement, as for the usual multi-pass attribute grammars, that all occurrences of the same attribute are computed in the same pass. It is shown that the problem of determining whether an arbitrary attribute grammar is pure multipass, is of inherently exponential time complexity. For fixed k > 0, it can be decided in polynomial time whether an attribute grammar is pure k-pass. The proofs are based on a characterization of pure multi-pass attribute grammars in terms of paths through their dependency graphs. A general result on dependency paths of attribute grammars relates them to (finite-copying) top-down tree transducers. The formal power of k-pass attribute grammars increases with increasing k. Formally, multi-pass attribute grammars are less powerful than arbitrary attribute grammars.