= Hydraulic System Planning - 2 (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 opens 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 set of jets j1...jn, 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.

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 uses 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(s) to achieve:

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

In output, a sequence of atoms of the form

    * {{{switchon(v, t)}}}.

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

== Predicates ==

 * '''Input''': {{{tank/1, jet/1, junction/1, valve/1, link/3, numValves/1, full/1, leaking/1, goal/1}}}

 * '''Output''': {{{switchon/2}}}

== Input format ==

== Output format ==

== Example(s) ==

== Note ==

With respect to the version of this problem as of the 2nd ASP Competition, there can be more than one goal per instance.

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