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 college, Germany. It encompasses a gate point building of a multi-core laptop with pipelined MIPS processor cores and a sequentially constant shared memory.

The booklet comprises 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 tips on how to the formal verification of synthesizable for multi-core processors within the future.

Constructions are in a gate point version and hence deterministic. against this the reference types 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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**Extra resources for A Pipelined Multi-core MIPS Machine: Hardware Implementation and Correctness Proof**

**Example text**

We now conclude that s(a) is well deﬁned by the second and third rules. 2 Some Basic Circuits Boolean expressions can be translated into circuits in a very intuitive way. In Fig. 5(b) we have translated the simple formulas from (4) for c (a, b, c) and s(a, b, c) into a circuit. With inputs (a, b, c) and outputs (c , s) this circuit satisﬁes c ,s = a+ b + c . A circuit satisfying this condition is called a full adder. We use the symbol from Fig. 5(a) to represent this circuit in subsequent constructions.

If e and e are boolean expressions then so is (e ◦ e ), where ◦ is a binary connector: e, e ∈ BE ∧ ◦ ∈ {∧, ∨, ⊕} → (e ◦ e ) ∈ BE . 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.

5 Drivers and Main Memory 55 yin yin α OC y y α β β Fig. 27. Open collector driver and its timing diagram collector drivers, and main memory. 5 that a design that works in the digital model also works in the detailed hardware model. For tristate drivers and main memory this will not be the case. 1 Open Collector Drivers and Active Low Signal A single open collector driver y and its detailed timing is shown in Fig. 27. If the input yin is 0, then the open collector driver also outputs 0. If the input is 1, then the driver is disabled.

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

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