A Coalgebraic Decision Procedure for NetKAT

Foster, Nate; Kozen, Dexter; Milano, Matthew; Silva, Alexandra; Thompson, Laure

doi:10.1145/2676726.2677011

Cited by 78 publications

(74 citation statements)

References 32 publications

(18 reference statements)

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“…Real-world networks often exhibit nondeterministic behaviors such as fault tolerant routing schemes to handle unexpected failures [34] and randomized algorithms to balance load across multiple paths [30]. Verifying that networks behave as expected in these more complicated scenarios requires a form of probabilistic reasoning, but most state-of-the-art network verification tools model only deterministic behaviors [14,25,27].…”

Section: Overviewmentioning

confidence: 99%

“…Whereas state-of-the-art tools can easily handle deterministic networks with hundreds of thousands of nodes, probabilistic tools are currently orders of magnitude behind. This paper presents McNetKAT, a new tool for reasoning about probabilistic network programs written in the guarded and history-free fragment of Probabilistic NetKAT (ProbNetKAT) [4,13,14,46]. ProbNetKAT is an expressive programming language based on Kleene Algebra with Tests, capable of modeling a variety of probabilistic behaviors and properties including randomized routing [30,48], uncertainty about demands [40], and failures [19].…”

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confidence: 99%

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Scalable verification of probabilistic networks

Smolka

Kumar

Kahn

et al. 2019

Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation

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This paper presents McNetKAT, a scalable tool for verifying probabilistic network programs. McNetKAT is based on a new semantics for the guarded and history-free fragment of Probabilistic NetKAT in terms of finite-state, absorbing Markov chains. This view allows the semantics of all programs to be computed exactly, enabling construction of an automatic verification tool. Domain-specific optimizations and a parallelizing backend enable McNetKAT to analyze networks with thousands of nodes, automatically reasoning about general properties such as probabilistic program equivalence and refinement, as well as networking properties such as resilience to failures. We evaluate McNetKAT's scalability using real-world topologies, compare its performance against state-of-the-art tools, and develop an extended case study on a recently proposed data center network design.

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Section: Overviewmentioning

confidence: 99%

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confidence: 99%

Scalable verification of probabilistic networks

Smolka

Kumar

Kahn

et al. 2019

Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation

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“…Another aspect of CKA that is not yet developed to the extent of KA is the coalgebraic perspective. We intend to investigate whether the coalgebraic tools developed for KA can be extended to CKA, which will hopefully lead to efficient bisimulation-based decision procedures [2,5].…”

Section: Proof We Begin Bymentioning

confidence: 99%

Concurrent Kleene Algebra: Free Model and Completeness

Kappé

Brunet

Silva

et al. 2018

Lecture Notes in Computer Science

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Concurrent Kleene Algebra (CKA) was introduced by Hoare, Moeller, Struth and Wehrman in 2009 as a framework to reason about concurrent programs. We prove that the axioms for CKA with bounded parallelism are complete for the semantics proposed in the original paper; consequently, these semantics are the free model for this fragment. This result settles a conjecture of Hoare and collaborators. Moreover, the technique developed to this end allows us to establish a Kleene Theorem for CKA, extending an earlier Kleene Theorem for a fragment of CKA. ments.The notion of N-freeness for pomsets is useful for proving the lemmas to come.Definition A.1. Let U = [u] be a pomset. We say that U is N-free if there are no u 0 , u 1 , u 2 , u 3 ∈ S u such that u 0 ≤ u u 1 , u 2 ≤ u u 3 and u 0 ≤ u u 3 and no other relation between them, i.e., the graph of these elements has the shape of an N.Note that N-freeness is well-defined for pomsets, for the presence of an Nshape does not depend on the particular representative u. It is not hard to see that all series-parallel pomsets are N-free. Perhaps surprisingly, this N-freeness provides a complete characterisation of series-parallel pomsets [6].It is also useful to restrict a labelled poset to a part of its carrier, as follows.Definition A.2. Let u be a labelled poset, and let S ⊆ S u . We write u ↾ S for the restriction of u to S, i.e., labelled poset given by S u↾S = S, ≤ u↾S = ≤ u ∩ S × S, and λ u↾S (z) = λ u (z).A.1 Subsumption of empty or primitive pomsets Lemma A.2. Let u be a labelled poset such that u ⊑ 1 or 1 ⊑ u. Then u = 1.Proof. We treat the case where u ⊑ 1; the case where 1 ⊑ u is similar. Let h : 1 → u witness that u ⊑ 1. Then h is a bijection from S 1 = ∅ to S u ; accordingly, S u = ∅. But then u = 1, because the labelled poset with empty carrier is unique.Proof. First, suppose that U = 1. We then have that U = [1] and V = [v] such that u ⊑ 1 or 1 ⊑ u. By Lemma A.2, we find that v = 1 and thus V = [1] = 1.Second, suppose that U = a for some a ∈ Σ. Then U = [u] for some pomset with singleton carrier S u , with λ u (u) = a for all u ∈ S u . Since V = [v] and u ⊑ v or v ⊑ u, we find that u ≃ v by Lemma A.3. This establishes that U = V . A.2 The factorisation lemmaLemma 3.3 (Factorisation). Let U , V 0 , and V 1 be pomsets such that U is subsumed by V 0 · V 1 . Then there exist pomsets U 0 and U 1 such that:Also, if U 0 , U 1 and V are pomsets such that U 0 U 1 ⊑ V , then there exist pomsets V 0 and V 1 such that:Proof. We start with the first claim. Let U , V 0 and V 1 be as in the premise, and write U = [u], V 0 = [v 0 ] and V 1 = [v 1 ]. Without loss of generality, we can assume that v 0 and v 1 are disjoint, that S v0 ∪ S v1 = S u , and that the identity function S v0 ∪ S v1 → S u is the subsumption witnessing that u ⊑ v 0 · v 1 .We then choose u i = u ↾ vi for i ∈ 2, and claim that u 0 · u 1 = u.-For the carrier, we already know that

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“…It is a known fact that formal foundations can play an important role in guiding the development of programming languages and associated verification tools, in accordance with an intended semantics obeying essential (behavioural) laws. Correspondingly, the current paper is targeting NetKAT [1,11] -a formal framework for specifying and reasoning about networks, integrated within the Frenetic suite of network management tools [10]. More precisely, we will exploit the sound and complete axiomatisation of NetKAT in [1] in order to derive explanations of safety failures in a purely equational fashion.…”

Section: Introductionmentioning

confidence: 99%

Explaining SDN Failures via Axiomatisations

Caltais

2019

Electron. Proc. Theor. Comput. Sci.

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This work introduces a concept of explanations with respect to the violation of safe behaviours within software defined networks (SDNs) expressible in NetKAT. The latter is a network programming language that is based on a well-studied mathematical structure, namely, Kleene Algebra with Tests (KAT). Amongst others, the mathematical foundation of NetKAT gave rise to a sound and complete equational theory. In our setting, a safe behaviour is characterised by a NetKAT policy which does not enable forwarding packets from ingress to an undesirable egress. Explanations for safety violations are derived in an equational fashion, based on a modification of the existing NetKAT axiomatisation.

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A Coalgebraic Decision Procedure for NetKAT

Cited by 78 publications

References 32 publications

Scalable verification of probabilistic networks

Scalable verification of probabilistic networks

Concurrent Kleene Algebra: Free Model and Completeness

Explaining SDN Failures via Axiomatisations

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