You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
When programming network functions, changes within a packet tend to have consequences---side effects which must be accounted for by network programmers or administrators via arbitrary logic and an innate understanding of dependencies. Examples of this include updating checksums when a packet's contents has been modified or adjusting a payload length field of a IPv6 header if another header is added or updated within a packet. While static-typing captures interface specifications and how packet contents should behave, it does not enforce precise invariants around runtime dependencies like the examples above. Instead, during the design phase of network functions, programmers should be given a easier way to specify checks up front, all without having to account for and keep track of these consequences at each and every step during the development cycle. In keeping with this view, we present a unique approach for adding and generating both static checks and dynamic contracts for specifying and checking packet processing operations. We develop our technique within an existing framework called NetBricks and demonstrate how our approach simplifies and checks common dependent packet and header processing logic that other systems take for granted, all without adding much overhead during development.

Cited Abstract(s):
[1]: We tackle the problem of deciding whether two probabilistic programs are equivalent in Probabilistic NetKAT, a formal language for specifying and reasoning about the behavior of packet-switched networks. We show that the problem is decidable for the history-free fragment of the language by developing an effective decision procedure based on stochastic matrices. The main challenge lies in reasoning about iteration, which we address by designing an encoding of the program semantics as a finite-state absorbing Markov chain, whose limiting distribution can be computed exactly. In an extended case study on a real-world data center network, we automatically verify various quantitative properties of interest, including resilience in the presence of failures, by analyzing the Markov chain semantics.

[2]: We present the design and implementation of p4v, a practical tool for verifying data planes described using the P4 programming language. The design of p4v is based on classic verification techniques but adds several key innovations including a novel mechanism for incorporating assumptions about the control plane and domain-specific optimizations which are needed to scale to large programs. We present case studies showing that p4v verifies important properties and finds bugs in real-world programs. We conduct experiments to quantify the scalability of p4v on a wide range of additional examples. We show that with just a few hundred lines of control-plane annotations, p4v is able to verify critical safety properties for switch.p4, a program that implements the functionality of on a modern data center switch, in under three minutes.

[3]: Recent years have seen growing interest in high-level languages for programming networks. But the design of these languages has been largely ad hoc, driven more by the needs of applications and the capabilities of network hardware than by foundational principles. The lack of a semantic foundation has left language designers with little guidance in determining how to incorporate new features, and programmers without a means to reason precisely about their code. This paper presents NetKAT, a new network programming language that is based on a solid mathematical foundation and comes equipped with a sound and complete equational theory. We describe the design of NetKAT, including primitives for filtering, modifying, and transmitting packets; union and sequential composition operators; and a Kleene star operator that iterates programs. We show that NetKAT is an instance of a canonical and well-studied mathematical structure called a Kleene algebra with tests (KAT) and prove that its equational theory is sound and complete with respect to its denotational semantics. Finally, we present practical applications of the equational theory including syntactic techniques for checking reachability, proving non-interference properties that ensure isolation between programs, and establishing the correctness of compilation algorithms.
Regarding type systems, languages, and other means to validate and verify network programs, we've already mentioned NetKat [3] earlier in this work, and there have been many follow-up pieces regarding the language, including probabilistic variants [1] . Just recently, p4v [2] was published and is motivated by real-world examples; it attempts to find bugs in P4 programs and verify program properties by incorporating domain-specific assumptions into a constraint solver.