14472583
An exercise in structural congruence
Milner's structural congruence is decidable for the pi-calculus without restriction, in exponential space.
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.
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.
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.
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.
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.
7110538
Only Persistence Makes Nonmonotonicity Monotonous
An important characteristic of many logics for artificial intelligence is that they are nonmonotonic. This means that adding a formula to the premises can destroy some of the consequences. There may exist formulae that can always be safely added to the premises without destroying any of the consequences: they respect monotonicity. We consider three preferential logics for which we analyze the class of formulae which respect monotonicity. For each of the three logics we show that this class is equal to the class of formulae preserved under going to more preferred models, and we provide syntactic characterizations of these classes.
32078047
Temporal Theories of Reasoning
In this paper we describe a general way of formalizing reasoning behaviour. Such a behaviour may be described by all the patterns which are valid for the behaviour. A pattern can be seen as a sequence of information states which describe what has been derived at each time point. A transition from an information state at a point in time to the state at the (or a) next time point is induced by one or more inference steps. We choose to model the information states by partial models and the patterns either by linear time or branching time temporal models. Using temporal logic one can define theories and look at all models of that theory. For a number of examples of reasoning behaviour we have been able to define temporal theories such that its (minimal) models correspond to the valid patterns of the behaviour. These theories prescribe that the inference steps which are possible, are "executed" in the temporal model. The examples indicate that partial temporal logic is a powerful means of describing and formalizing complex reasoning patterns, as the dynamic aspects of reasoning systems are integrated into the static ones in a clear fashion.
15030192
Nonmonotonic reasoning with multiple belief sets
In complex reasoning tasks it is often the case that there is no single, correct set of conclusions given some initial information. Instead, there may be several such conclusion sets, which we will call belief sets. In the present paper we introduce nonmonotonic belief set operators and selection operators to formalize and to analyze structural aspects of reasoning with multiple belief sets. We define and investigate formal properties of belief set operators as absorption, congruence, supradeductivity and weak belief monotony. Furthermore, it is shown that for each belief set operator satisfying strong belief cumulativity there exists a largest monotonic logic underlying it, thus generalizing a result for nonmonotonic inference operations. Finally, we study abstract properties of selection operators connected to belief set operators, which are used to choose some of the possible belief sets.
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.
30357320
The Power to Two-Way Deterministic Checking Stack Automata
Abstract It is well known that nondeterministic two-way checking stack automata recognize NSPACE( n ). We show that deterministic two-way checking stack automata have the same power as deterministic two-way two-head finite automata. The easy proof is based on the closure under inverse deterministic two-way GSM mappings of the deterministic two-way two-head finite automaton languages.