Mechanical Verification of an Ideal Incremental ABR Conformance Algorithm

Abstract

Abstract. The Available Bit Rate protocol (ABR) for ATM networks is well-adapted to data traffic by providing minimum rate guarantees and low cell loss to the ABR source end system. An ABR conformance algorithm for controlling the source rates through an interface has been defined by ATM Forum and a more efficient version of it has been designed in [13]. We present in this work the first complete mechanical verification of the equivalence between these two algorithms. The proof is involved and has been supported by the PVS theorem-prover. It has required many lemmas, case analysis and induction reasoning for the manipulation of unbounded scheduling lists. Some ABR conformance protocols have been verified in previous works. However these protocols are approximations of the one we consider here. For instance, the algorithms mechanically proved in [10] and [5] consider scheduling lists with only two elements.

Automated Certification of Implicit Induction Proofs

“….. In [15,17], Acr1 has been shown equivalent to Acr, i.e. for any configuration of the RM-cell buffer and any time t, both algorithms compute the same conformity value.…”

“…The conjecture [301] sortedT (u 1 ) = T rue ⇒ sortedT (insAt(u 1 , u 2 , u 3 )) = T rue, denoted by sorted insat1 in [17], will be proved with the inference system from Fig. 1 and the axioms from subsection 4.1, using the lemmas , u 9 ).…”

“…The same inference system and proof strategy involved in the proof of sorted insat1 have been applied to prove other Spike conjectures involved in the ABR proof from [17]. In Table 1, we give some statistics about the proofs that have been automatically certified by Coq.…”

“…In Table 1, we give some statistics about the proofs that have been automatically certified by Coq. We firstly list the name of the conjectures, as denoted in [17]. Then, for the proof of each conjecture, we show how many times each of the Spike inference rules has been applied, the number of needed lemmas, the size of the list of functionals for the main proof, and the global time of the certification process (lemmas + conjecture).…”

“…The case study of our choice is the validation proof of a conformance algorithm for the ABR protocol [14]. An interactive proof using PVS [18] was firstly presented in [16], then it has been shown in [17] that more than a third of the user interactions can be avoided using implicit induction techniques, Spike succeeding to prove 60% of the user-provided lemmas automatically. Now, a simpler but more restrictive version of the Spike inference system has been shown powerful enough to prove 2/3 out of these lemmas.…”