= Hydraulic Leaking =

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== Problem Description ==
A simplified version of the hydraulic system on a space shuttle consists of a directed graph, G, such that:

    * Nodes of this graph are labeled as tanks,jets, or junctions.
    * Every link between two nodes is labeled by a valve.
    * There are no paths in G between any two tanks.
    * For every jet there always is a path in G from a tank to this jet.

Tanks can be full or empty. Valves can be open or closed. Some of the valves may be leaking. A state of G is specified by the set of full tanks, the set of open valves, and the set of leaking valves. A node of G is called pressurized in state S if it is a full tank or if there exists a path from some full tank of G to this node such that all the valves on the edges of this path are open.

We assume that in a state S a shuttle controller can open a valve V2 corresponding to a directed link <N1,N2> only if N1 is pressurized. (Note, a leaking valve can be opened.)

Problem: Given a graph G together with a initial state of G and a jet j, a shuttle controller needs to find a shortest plan among those using the least number of leaking valves. Write a program which automates this process.


== Input format ==

The graph should be described by the collection of ground atoms:

    * tank(t): t is a tank
    * jet(j): j is a jet
    * junction(p): p is a junction
    * valve(v): v is a valve
    * link(n1, n2, v): v is the valve on the pipe connecting node n1 and n2.
    * numValves(n): n is the total number of valves in the graph

The state description should use atoms:

    * full(t) iff tank t is full. A tank is empty if it is not mentioned to be full in the input.
    * leaking(v) iff valve v is leaking. A valve is not leaking if it is not mentioned to be leaking in the input.

The goal to achieve:

    * goal(j): jet j needs to be pressurized

== Output format ==

A sequence of atoms of the form

    * switchon(v, t).

which means to open valve v at time step t. The switches should occur at consecutive time steps beginning from 0.


== Comment ==

Comment: This problem took part in the Second ASP Competition and was proposed by Michael Gelfond, Ricardo Morales and Yuanlin Zhang. 

== Example ==

== Author(s) ==
 * Francesco Calimeri 	
  * University of Calabria, Italy
 * Maria Carmela Santoro 	
  * University of Calabria, Italy