#lang karp/problem-definition

(require karp/lib/graph
         karp/lib/graph-inspector)

(decision-problem #:name iset
                  #:instance ([G is-a graph]
                              [k is-a natural])
                  #:certificate (subset-of (vertices-of G)) )

; there is one small bug in the code below, can you find it?
#;(define-iset-verifier iset-inst iset-cert
  (and
   (∀ [e ∈ (edges-of (G iset-inst))]
      (nand (set-∈ (e-u e) iset-cert)
            (set-∈ (e-v e) iset-cert)))
   (<= (set-size iset-cert) (k iset-inst))))

; the same bug below
(define-iset-verifier iset-inst iset-cert
  (and
   (∀ [u ∈ iset-cert]
      (∀ [v ∈ iset-cert]
         (set-∉ u (neighbors (G iset-inst) v))))
   (<= (set-size iset-cert) (k iset-inst))))