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Thanks for the detailed explanation. It's interesting to note that firewall rules are well captured in the predicate logic.

Just curious: Have you encountered rules that cannot be cast into predicate logic framework in Z3?

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I've not. Firewall rules are of the form {predicate} -> {decision}, where {decision} is block/allow and {predicate} defines a set of packets: something like a source address range, source port range, destination address range, destination port range, and protocol. When a packet comes in, the firewall finds all matching predicates (there can be multiple) and makes a block/allow decision. Since checking for packet-predicate matches is done with simple and/or/not formulas, I can't think of a rule which could not be expressed in Z3. Also, this is hardly taxing Z3: it supports reasoning with real numbers and nonlinear constraints.

Thanks again. I didn't know Z3 could handle formulae with real numbers. I will take a closer look at it. :)

On the network firewall rules (at multi-tenant Azure, I presume), what were Z3's runtimes look like?

Z3 was able to check equivalence of firewalls with a few hundred rules in a fraction of a second on a standard workstation. I was extremely impressed, especially since the brute-force IPv4 packet search space is 2^112! There's some wizardry going on beneath the hood.

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