7,125 research outputs found
State space c-reductions for concurrent systems in rewriting logic
We present c-reductions, a state space reduction technique.
The rough idea is to exploit some equivalence relation on states (possibly capturing system regularities) that preserves behavioral properties, and explore the induced quotient system. This is done by means of a canonizer
function, which maps each state into a (non necessarily unique) canonical representative of its equivalence class. The approach exploits the expressiveness of rewriting logic and its realization in Maude to enjoy several advantages over similar approaches: exibility and simplicity in
the definition of the reductions (supporting not only traditional symmetry reductions, but also name reuse and name abstraction); reasoning support for checking and proving correctness of the reductions; and automatization
of the reduction infrastructure via Maude's meta-programming
features. The approach has been validated over a set of representative case studies, exhibiting comparable results with respect to other tools
Meta-F*: Proof Automation with SMT, Tactics, and Metaprograms
We introduce Meta-F*, a tactics and metaprogramming framework for the F*
program verifier. The main novelty of Meta-F* is allowing the use of tactics
and metaprogramming to discharge assertions not solvable by SMT, or to just
simplify them into well-behaved SMT fragments. Plus, Meta-F* can be used to
generate verified code automatically.
Meta-F* is implemented as an F* effect, which, given the powerful effect
system of F*, heavily increases code reuse and even enables the lightweight
verification of metaprograms. Metaprograms can be either interpreted, or
compiled to efficient native code that can be dynamically loaded into the F*
type-checker and can interoperate with interpreted code. Evaluation on
realistic case studies shows that Meta-F* provides substantial gains in proof
development, efficiency, and robustness.Comment: Full version of ESOP'19 pape
Hochschild (co)homology of the Dunkl operator quantization of -singularity
We study Hochschild (co)homology groups of the Dunkl operator quantization of
-singularity constructed by Halbout and Tang. Further, we study traces on
this algebra and prove a local algebraic index formula.Comment: 26 pages. Comments and suggestions welcome. Some typos and other
minor mistakes correcte
A formally verified proof of the prime number theorem
The prime number theorem, established by Hadamard and de la Vall'ee Poussin
independently in 1896, asserts that the density of primes in the positive
integers is asymptotic to 1 / ln x. Whereas their proofs made serious use of
the methods of complex analysis, elementary proofs were provided by Selberg and
Erd"os in 1948. We describe a formally verified version of Selberg's proof,
obtained using the Isabelle proof assistant.Comment: 23 page
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