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

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

The booklet includes the 1st correctness proofs for either the gate point implementation of a multi-core processor and likewise of a cache established sequentially constant shared reminiscence. This opens easy methods to the formal verification of synthesizable for multi-core processors within the future.

Constructions are in a gate point version and therefore deterministic. against this the reference types opposed to which correctness is proven are nondeterministic. the advance of the extra equipment for those proofs and the correctness evidence of the shared reminiscence on the gate point are the most technical contributions of this work.

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**Extra resources for A Pipelined Multi-core MIPS Machine Hardware Implementation and Correctness Proof**

**Example text**

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 ∨. Thus, x1 ∧x2 ∨x3 is an abbreviation for x1 ∧ x2 ∨ x3 = ((x1 ) ∧ x2 ) ∨ x3 . We denote expressions e depending on variables x = x[1 : n] by e(x). Variables xi can take values in B. Thus, x = x[1 : n] can take values in Bn .

We denote expressions e depending on variables x = x[1 : n] by e(x). Variables xi can take values in B. Thus, x = x[1 : n] can take values in Bn . We denote the result of evaluation of expression e ∈ BE with a bit-string a ∈ Bn of inputs by e(a) and get a straightforward set of rules for evaluating expressions: 22 2 Number Formats and Boolean Algebra 1. Substitute ai for xi : xi = ai . 2. If e = (e ), then evaluate e(a) by evaluating e (a) and negating the result according to the predeﬁned meaning of negation in Table 3: (e )(a) = e (a) .

Usually, a physical register will settle in this situation quickly into an unknown logical value, but in rare occasions the register can “hang” at a voltage level not recognized as 0 or 1 for a long time. This is called ringing or metastability. Formally, we deﬁne the register semantics of the detailed hardware model in the following way: ⎧ a[i] reset(t) ⎪ ⎪ ⎪ ⎪ ⎪ x[i]in(e(c)) t ∈ [e(c) + σ, e(c + 1) + ρ] ∧ stable(x[i]in, c) ⎪ ⎪ ⎪ ⎨ ∧ stable(x[i]ce, c) ∧ x[i]ce(e(c)) ∧ ¬reset(t) x[i](t) = ⎪ x[i](e(c)) t ∈ (e(c) + ρ, e(c + 1) + ρ] ∧ stable(x[i]ce, c) ⎪ ⎪ ⎪ ⎪ ⎪ ∧ ¬x[i]ce(e(c)) ∧ ¬reset(t) ⎪ ⎪ ⎩ Ω otherwise .