Question

Question:Show how to implement the stingy algorithm for Horn formula satisfiability (Section 5.3) in time that is linear in the length of the formula (the number of occurrences of literals in it). (Hint: Use a directed graph, with one node per variable, to represent the implications.)

Short answer

Answer:This challenge of determining whether such a combination of conceptual Horn sentences seems to be satisfiable or not is known as Horn-satisfiability. The indicated literals are the simplest representation of something like the Horn formula.

Step-by-step solution

Build direct bipartiate(graph):

The entire process runs in linear time since each literal is only marked true once (with respect to the number of literals, because of the graph building).

Build a directed(bipartiate) graph, connecting the Horn clauses to their respective positive literal(if they have one), and connecting the literals to all chauses where they appear negated.

 Calculation of Propagate for programme functionality:

[UPDATE] Do the same for each clause c that does not contain a negating literal. {

assuming c doesn't have a significant literal STOPunsatisfactory,

disseminate the otherwise (c)

}

eventually, this unit programme functionality

propagate(c) :-

suppose c(positive )'s literal hasn't been certified true yet {

mark p true

considering all(p,c') in the graph's Edge set {

remove p from c'

Disseminate if c' contains nothing more negated literals (c')
}

}

Percussion seems to be the task of deciding whether a given mixture of theoretical Horn sentences appears to really be satisfiable or not. The literals shown are the most basic representations of things like with the Horn formula.