25 research outputs found
An automata characterisation for multiple context-free languages
We introduce tree stack automata as a new class of automata with storage and
identify a restricted form of tree stack automata that recognises exactly the
multiple context-free languages.Comment: This is an extended version of a paper with the same title accepted
at the 20th International Conference on Developments in Language Theory (DLT
2016
Automata with Nested Pebbles Capture First-Order Logic with Transitive Closure
String languages recognizable in (deterministic) log-space are characterized
either by two-way (deterministic) multi-head automata, or following Immerman,
by first-order logic with (deterministic) transitive closure. Here we elaborate
this result, and match the number of heads to the arity of the transitive
closure. More precisely, first-order logic with k-ary deterministic transitive
closure has the same power as deterministic automata walking on their input
with k heads, additionally using a finite set of nested pebbles. This result is
valid for strings, ordered 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. For nondeterministic automata, the logic is restricted to
positive occurrences of transitive closure.
The special case of k=1 for trees, shows that single-head deterministic
tree-walking automata with nested pebbles are characterized by first-order
logic with unary deterministic transitive closure. This refines our earlier
result that placed these automata between first-order and monadic second-order
logic on trees.Comment: Paper for Logical Methods in Computer Science, 27 pages, 1 figur
Regular Separability and Intersection Emptiness Are Independent Problems
The problem of regular separability asks, given two languages K and L, whether there exists a regular language S that includes K and is disjoint from L. This problem becomes interesting when the input languages K and L are drawn from language classes beyond the regular languages. For such classes, a mild and useful assumption is that they are full trios, i.e. closed under rational transductions.
All the results on regular separability for full trios obtained so far exhibited a noteworthy correspondence with the intersection emptiness problem: In each case, regular separability is decidable if and only if intersection emptiness is decidable. This raises the question whether for full trios, regular separability can be reduced to intersection emptiness or vice-versa.
We present counterexamples showing that neither of the two problems can be reduced to the other. More specifically, we describe full trios C_1, D_1, C_2, D_2 such that (i) intersection emptiness is decidable for C_1 and D_1, but regular separability is undecidable for C_1 and D_1 and (ii) regular separability is decidable for C_2 and D_2, but intersection emptiness is undecidable for C_2 and D_2
A B\"uchi-Elgot-Trakhtenbrot theorem for automata with MSO graph storage
We introduce MSO graph storage types, and call a storage type MSO-expressible
if it is isomorphic to some MSO graph storage type. An MSO graph storage type
has MSO-definable sets of graphs as storage configurations and as storage
transformations. We consider sequential automata with MSO graph storage and
associate with each such automaton a string language (in the usual way) and a
graph language; a graph is accepted by the automaton if it represents a correct
sequence of storage configurations for a given input string. For each MSO graph
storage type, we define an MSO logic which is a subset of the usual MSO logic
on graphs. We prove a B\"uchi-Elgot-Trakhtenbrot theorem, both for the string
case and the graph case. Moreover, we prove that (i) each MSO graph
transduction can be used as storage transformation in an MSO graph storage
type, (ii) every automatic storage type is MSO-expressible, and (iii) the
pushdown operator on storage types preserves the property of
MSO-expressibility. Thus, the iterated pushdown storage types are
MSO-expressible
Top-down tree transducers with two-way tree walking look-ahead
AbstractWe consider top-down tree transducers with deterministic, nondeterministic and universal two-way tree walking look-ahead and compare the transformational powers of their deterministic and strongly deterministic versions by giving the inclusion diagram of the induced tree transformation classes. We also study the closure properties of these transformation classes with respect to composition
Deciding Linear Height and Linear Size-to-Height Increase for Macro Tree Transducers
In this paper we study Macro Tree Transducers (MTT), specifically the Linear
Height Increase ("LHI") and Linear input Size to output Height ("LSHI")
constraints. In order to decide whether a Macro tree transducer (MTT) is of LHI
or LSHI, we define a notion of depth-properness: a MTT is depth-proper if, for
each state, there is no bound to the depth at which it places its argument
trees. We show how to effectively put a MTT in depth-proper form. For MTTs in
Depth-proper form, we characterize the LSH property as equivalent to the
finite-nesting property, and we characterize the LHI property as equivalent to
the finiteness of a new type of nesting which we call Multi-Leaf-nesting (or
ML-nesting). As opposed to regular nesting where we look at the nesting of
states applied to a single input node, we count the nesting of states applied
to nodes that are not ancestors of each other. We use this characterization to
give a decision procedure for the LSHI and LHI properties. Finally we consider
the decision problem of the LSOI (Linear input Size to number of distinct
Output subtrees Increase) property. A long standing open problem is whether MTT
of LSOI are as expressive as Attribute Tree Transducers (ATT), in this paper we
show that deciding whether a MTT is of LSOI is as hard as deciding the
equivalence of ATTs