22 research outputs found
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
MSO Undecidability for some Hereditary Classes of Unbounded Clique-Width
Seese's conjecture for finite graphs states that monadic second-order logic
(MSO) is undecidable on all graph classes of unbounded clique-width. We show
that to establish this it would suffice to show that grids of unbounded size
can be interpreted in two families of graph classes: minimal hereditary classes
of unbounded clique-width; and antichains of unbounded clique-width under the
induced subgraph relation. We explore a number of known examples of the former
category and establish that grids of unbounded size can indeed be interpreted
in them.Comment: 23 page
Model Checking Communicating Processes: Run Graphs, Graph Grammars, and MSO
The formal model of recursive communicating processes (RCPS) is important in practice but does not allows to derive decidability results for model checking questions easily. We focus a partial order representation of RCPSâs execution by graphsâso called run graphs, and suggest an underapproximative verification approach based on a bounded-treewidth requirement. This allows to directly derive positive decidability results for MSO model checking (seen as partial order logic on run graphs) based on a context-freeness argument for restricted classes run graph
On the Path-Width of Integer Linear Programming
We consider the feasibility problem of integer linear programming (ILP). We
show that solutions of any ILP instance can be naturally represented by an
FO-definable class of graphs. For each solution there may be many graphs
representing it. However, one of these graphs is of path-width at most 2n,
where n is the number of variables in the instance. Since FO is decidable on
graphs of bounded path- width, we obtain an alternative decidability result for
ILP. The technique we use underlines a common principle to prove decidability
which has previously been employed for automata with auxiliary storage. We also
show how this new result links to automata theory and program verification.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Automata and temporal logic over arbitrary linear time
Linear temporal logic was introduced in order to reason about reactive
systems. It is often considered with respect to infinite words, to specify the
behaviour of long-running systems. One can consider more general models for
linear time, using words indexed by arbitrary linear orderings. We investigate
the connections between temporal logic and automata on linear orderings, as
introduced by Bruy\`ere and Carton. We provide a doubly exponential procedure
to compute from any LTL formula with Until, Since, and the Stavi connectives an
automaton that decides whether that formula holds on the input word. In
particular, since the emptiness problem for these automata is decidable, this
transformation gives a decision procedure for the satisfiability of the logic
The First-Order Theory of Ground Tree Rewrite Graphs
We prove that the complexity of the uniform first-order theory
of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n). Providing a matching lower bound, we show that there is some
fixed ground tree rewrite graph whose first-order theory is hard
for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single unary predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory
Some Remarks on Deciding Equivalence for Graph-To-Graph Transducers
We study the following decision problem: given two mso transductions that input and output graphs of bounded treewidth, decide if they are equivalent, i.e. isomorphic inputs give isomorphic outputs. We do not know how to decide it, but we propose an approach that uses automata manipulating elements of a ring extended with division. The approach works for a variant of the problem, where isomorphism on output graphs is replaced by a relaxation of isomorphism