text: abstraction of a trace, as defined in definition 9. in
  fact, an a-trace can be obtained from a given trace by removing its actions and keeping only the number
  of jumps.
  definition 20 ((τ ,ε )-closeness [3]) consider a test duration t ∈ r+ , a maximum number of jumps j ∈
  n, and τ , ε > 0; then two a-traces y1 and y2 are said to be (τ ,ε )-close, denoted by y1 ≈(τ ,ε ) y2 , if
  1. for all (t, i) ∈ dom(y1 ) with t ≤ t, i ≤ j, there exists (s, j) ∈ dom(y2 ) such that |t − s| ≤ τ and
  ky1 (t, i) − y2 (s, j)k ≤ ε , and
  2. for all (t, i) ∈ dom(y2 ) with t ≤ t, i ≤ j, there exists (s, j) ∈ dom(y1 ) such that |t − s| ≤ τ and
  ky2 (t, i) − y1 (s, j)k ≤ ε .
  definition 21 (conformance relation [3]) consider two hybrid i/o automata h1 and h2 . given a
  test duration t ∈ r+ , a maximum number of jumps j ∈ n, and τ , ε > 0, h2 conforms to h1 , denoted by
  h2 ≈(τ ,ε ) h1 , if and only if for all solution pairs (u, y1 ) of h1 , there exists a solution pair (u, y2 ) of h2
  such that the corresponding output a-traces y1 and y2 are (τ ,ε )-close.
  figure 2 shows two a-traces y1 and y2 where y1 ≈(0.8,1) y2 . as mentioned, the notion of hconf (≈(τ ,ε ) )
  is not sensitive to the existence/absence of actions. as a result, if the hioa generating y1 produces
  output action off at t = 2 and the other hioa produces no action, the two a-traces are still regarded as
  conforming according to hconf.
  1 in