By Mikhail Kovalev, Silvia M. Müller, Wolfgang J. Paul

ISBN-10: 3319139053

ISBN-13: 9783319139050

ISBN-10: 3319139061

ISBN-13: 9783319139067

This monograph relies at the 3rd author's lectures on computing device structure, given in the summertime semester 2013 at Saarland collage, Germany. It incorporates a gate point building of a multi-core laptop with pipelined MIPS processor cores and a sequentially constant shared memory.

The ebook includes the 1st correctness proofs for either the gate point implementation of a multi-core processor and in addition of a cache dependent sequentially constant shared reminiscence. This opens the best way to the formal verification of synthesizable for multi-core processors within the future.

Constructions are in a gate point version and hence deterministic. by contrast the reference versions opposed to which correctness is proven are nondeterministic. the improvement of the extra equipment for those proofs and the correctness facts of the shared reminiscence on the gate point are the most technical contributions of this work.

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**Additional info for A Pipelined Multi-core MIPS Machine: Hardware Implementation and Correctness Proof**

**Example text**

4. If fi is a symbol for a function with ni arguments, then we can obtain a Boolean expression fi (e1 , . . , eni ) by substituting the function arguments with Boolean expressions ej : (∀j ∈ [1 : ni ] : ej ∈ BE) → fi (e1 , . . , eni ) ∈ BE . 5. All Boolean expressions are formed by the above rules. We call a Boolean expression pure if it uses only the predeﬁned connectives and doesn’t use any other function symbols. In order to save brackets, one uses the convention that binds stronger than ∧ and that ∧ binds stronger than ∨.

The correctness can be checked in the usual brute force way by trying all 8 assignments of values in B3 to the variables of the expressions, or by applying the identities listed in Sect. 1. In the remainder of this book, we return to the usual mathematical notation, using the equality sign for both identities and equations to be solved. We will only use the equivalence sign when deﬁning predicates with the equality sign in the right-hand side. Whether we deal with identities or whether we solve equations will (hopefully) be clear from the context.

The extra hypothesis a − b ≥ 0 implies a − b ∈ Bn . 5. 6 Boolean Algebra We consider Boolean expressions with constants 0 and 1, variables x0 , x1 , . , a, b, . , and function symbols , ∧, ∨, ⊕, f (. ), g(. ), . .. Four of the function symbols have predeﬁned semantics as speciﬁed in Table 3. 6 Boolean Algebra 21 Table 3. Boolean operators x 0 0 1 1 y 0 1 0 1 x 1 1 0 0 x ∧ y x ∨ y x⊕y 0 0 0 0 1 1 0 1 1 1 1 0 C = {0, 1} V = {x0 , x1 , . } F = {f0 , f1 , . } . and denotes the number of arguments for function fi with ni .

### A Pipelined Multi-core MIPS Machine: Hardware Implementation and Correctness Proof by Mikhail Kovalev, Silvia M. Müller, Wolfgang J. Paul

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