Synergy User Manual and Tutorial. - THE CORE MEMORY

Synergy User Manual and Tutorial
Theory and Challenges of Parallel Programs and Performance
Evaluation
Basic Logic
Logic is the study of the reasoning of arguments and is both a branch of mathematics and
a branch of philosophy. In the mathematical sense, it is the study of mathematical
properties and relations, such as soundness and completeness of arguments. In the
philosophical sense, logic is the study of the correctness of arguments. A logic is
comprised of an informal language coupled with model-theoretic semantics and/or a
deductive system. The language allows the arguments to be stated, which is similar to
the way we state our thoughts in written or spoken languages. The semantics provide a
definition of possible truth-conditions for arguments and the deductive system provides
inferences that are correct for the given language.
This section introduces formal logics that can be used as methods to design program logic
and prove that the logic is sound. Systems based on propositional logic have been
produced to facilitate the design and proofs for sequential programs. However, these
systems were inadequate for concurrent applications. Variations of temporal logic, which
is based on modal logic, are used to evaluate the logic of concurrent programs.
Propositional Logic
Symbolic logic is divided into several parts of which propositional calculus is the most
fundamental. A proposition, or statement, is any declarative sentence, which is either
true or false. We refer to true (T) or false (F) as the truth-value of the statement.
“1 + 1 = 2” is a true statement.
“1 + 1 = 11” is a false statement.
“Tomorrow will be a sunny day” is a proposition whose truth is yet to be determined.
“The number 1” is not a proposition because it is not a sentence.
Simple statements are those that represent a single idea or subject and contain no other
statements within. Simple statements will be represented by the symbols: p, q, r and s. If
p stands for the proposition: “ice is cold”, we denote it as:
p: “ice is cold”,
which is read as:
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