A computer-checked verification of Milner's scheduler

Korver, H.P.; Springintveld, J.

doi:10.1007/3-540-57887-0_95

Cited by 21 publications

(24 citation statements)

References 6 publications

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“…We find descriptions along this line in verifications of the bakery protocol [GK94], Milner's scheduler [KS94], a leader election protocol [FGK97], grid protocols [BHP97], and a summing protocol [GMS97].…”

Section: Introductionmentioning

confidence: 89%

Confluence for process verification

Groote

Sellink

1995

CONCUR '95: Concurrency Theory

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This chapter addresses the question how to verify distributed and communicating systems in an effective way from an explicit process algebraic standpoint. This means that all calculations are based on the axioms and principles of the process algebras. The first step towards such verifications is to extend process algebra (ACP) with equational data types which adds required expressive power to describe distributed systems. Subsequently, linear process operators, invariants, the cones and foci method, the composition of many similar parallel processes, and the use of confluence are explained, as means to verify increasingly complex systems. As illustration, verifications of the serial line interface protocol (SLIP) and the IEEE 1394 tree identify protocol are included.

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Section: Introductionmentioning

confidence: 89%

Confluence for process verification

Groote

Sellink

1995

CONCUR '95: Concurrency Theory

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“…This section presents a brief overview of standard techniques that are used in these verifications. For verifications in the specification language µCRL [114] that use one or more of these techniques, see [56,98,111,140,186] Expansion. A basic technique in protocol verification is expansion [47] of the merge operator.…”

Section: Verification Techniquesmentioning

confidence: 99%

Introduction to Process Algebra

Fokkink

2000

Texts in Theoretical Computer Science. An EATCS Series

219

163

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“…In the context of process algebra [5] most such checks have been carried out using the language pCRL [34]. It has been encoded in the Coq system and applied to the verification of the alternating bit protocol [8, 7], Milner's scheduler [47], a bounded retransmission protocol [36] and parallel queues [48]. pCRL has also been encoded in PVS and a distributed summing protocol has been computer checked in [33] using the methodology presented in [35].…”

Section: Using Cones and Foci In Pvsmentioning

confidence: 99%

“…On a more concrete level, one finds in almost any proof -and correctness proofs of distributed systems or protocols are no exception -flaws that even may have impact on the correctness of the protocol. A typical example is the equality between an implementation and specification stated on page ll8 in [60] that was seen to be incorrect when a fully formalized proof was proof checked [47]. Using proof checkers can lead to a very strong emotion, which borders to addiction.…”

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confidence: 99%

Checking verifications of protocols and distributed systems by computer

Groote

Monin

Pol

1998

CONCUR'98 Concurrency Theory

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We provide a treatise about checking proofs of distributed systems by computer using general purpose proof checkers. In particular, we present two approaches to verifying and checking the verification of the Sequential Line Interface Protocol (SLIP), one using rewriting techniques and one using the so-called cones and foci theorem. Both verifications are carried out in the setting of process algebra. Finally, we present an overview of literature containing checked proofs. Note:The research of the second author is supported by Human Capital Mobility (HCM). Proof checkersAnyone trying to use a proof checker, e.g. Isabelle [67,68], HOL [29], Coq [20], PVS [78], Boyer-Moore [14] or many others that exist today has experienced the same frustration. It is very difficult to prove even the simplest theorem. In the first place it is difficult to get acquainted to the logical language of the system. Most systems employ higher order logics that are extremely versatile and expressive. However, before we can use the system, we must learn the syntax to express definitions and theorems and we must also learn the language to construct proofs.The second difficulty is to get used to strict logical rules that govern the reasoning allowed by the proof checker. Most of us have been educated in a mathematical style, which can be best described as intuitive reasoning with steps that are chosen to be sufficiently small to be acceptable by others.We all know examples of sound looking proofs of obviously wrong facts ('1 = -1', 'every triangle is isosceles', (in every group of people all members have the same age'). In fact it is quite common that mathematical proofs contain flaws. Especially, the correctness of distributed programs and protocols is a delicate matter due to their nondeterministic and discrete character. Proof checkers are intended to ameliorate this situation.One must get rid of the sloppiness of mathematical reasoning and get used to a more logical way of inferring facts. That is to say, one should not eliminate the mathematical intuition that helps guiding the proof, as the logical reasoning steps are so detailed that one easily looses track. And if this happens, even relatively short proofs, are impossible to find.A typical exercise that was carried out using Coq during our first encounters with theorem checkers, gives an impression of the time required to provide a formal proof. We wanted to show that there does not exist a largest prime number. A well known mathematical proof of this fact goes like this. 1 PROOF CHECKERS AND CONCURRENCY 2Suppose there exists a largest prime n. So, as now the product of all prime numbers exists, let it be m. Now consider m + 1. Clearly, dividing m + 1 by any prime number yields remainder 1, and therefore m + 1 is itself also a prime number, contradicting that n is the largest prime.The formal proof requires that first a definition of natural numbers, the induction principle, multiplication, dividahility and primality are given. Most theorem checkers contain nowadays libraries,...

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A computer-checked verification of Milner's scheduler

Abstract: We present an equational veri cation of Milner's scheduler, which w e c hecked by computer. To our knowledge this is the rst time that the scheduler is proof-checked for a general numbern of scheduled processes.

Cited by 21 publications

References 6 publications

Confluence for process verification

Confluence for process verification

Introduction to Process Algebra

Checking verifications of protocols and distributed systems by computer

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