= 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 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, and all valves are assumed to be all closed in their initial state.)

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.


== 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 ==

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

== Output format ==

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.

== Example(s) ==

INPUT
{{{
tank(t111). tank(t112). tank(t113).
jet(j1). jet(j2). jet(j3).
junction(p1). junction(p2). junction(p3). junction(p4). junction(p5). junction(p6).
valve(v1).  valve(v2).  valve(v3).  valve(v4).  valve(v5).
valve(v6).  valve(v7).  valve(v8).  valve(v9).  valve(v10).
valve(v11). valve(v12). valve(v13).
numValves(13).
link(t111, p1, v1).  link(p1, p2, v2).  link(p2, j1, v3).
link(t112, p3, v4).  link(p4, p3, v5).  link(p4, j2, v6).
link(t113, p5, v7).  link(p5, p6, v8).  link(p6, j3, v9).
link(p1, p3, v10). link(p3, p5, v11).
link(p4, p2, v12). link(p6, p4, v13). 
full(t111).  leaking(v2).  goal(j1).
}}}

OUTPUT
{{{
switchon(v1,0). switchon(v3,6). switchon(v8,3). switchon(v10,1). 
switchon(v11,2). switchon(v12,5). switchon(v13,4).
}}}

== Notes and Updates ==

With respect to the version of this problem as of the 2nd ASP Competition, there can be more than one goal per instance.
Note that valves are assumed to be all closed in their initial state.

It is important to point out that the Competition's instance family is such that each individual goal subgraph is disjoint (a tank can reach at most one goal). 

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