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Verification and Specification of Concurrent Programs
- A Decade of Concurrency - Reflexions and Perspectives, Springer Verlag (1993) 347–374 LNCS 803
, 1993
"... . I explore the history of, and lessons learned from, eighteen years of assertional methods for specifying and verifying concurrent programs. I then propose a Utopian future in which mathematics prevails. Keywords. Assertional methods, fairness, formal methods, mathematics, Owicki-Gries method, ..."
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. I explore the history of, and lessons learned from, eighteen years of assertional methods for specifying and verifying concurrent programs. I then propose a Utopian future in which mathematics prevails. Keywords. Assertional methods, fairness, formal methods, mathematics, Owicki-Gries method, temporal logic, TLA. Table of Contents 1 A Brief and Rather Biased History of State-Based Methods for Verifying Concurrent Systems . . . . . . . . . . . . . . . . . . 2 1.1 From Floyd to Owicki and Gries, and Beyond . . . . . . . . . . . 2 1.2 Temporal Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Unity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 An Even Briefer and More Biased History of State-Based Specification Methods for Concurrent Systems . . . . . . . . . 6 2.1 Axiomatic Specifications . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Operational Specifications . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Finite-State Methods ...
On Distributive Fixpoint Expressions
, 1998
"... For every fixpoint expression e of alternationdepth r, we construct a new fixpoint expression e 0 of alternation-depth 2 and size O(r \Delta jej). Expression e 0 is equivalent to e whenever operators are distributive and the underlying complete lattice has a co-continuous least upper bound. We ..."
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For every fixpoint expression e of alternationdepth r, we construct a new fixpoint expression e 0 of alternation-depth 2 and size O(r \Delta jej). Expression e 0 is equivalent to e whenever operators are distributive and the underlying complete lattice has a co-continuous least upper bound. We show that our transformation is optimal not only w.r.t. alternation-depth but also w.r.t. the increase in size of the resulting expression.
On Distributive Fixed-Point Expressions
, 1998
"... For every fixed-point expression e of alternation-depth r, we construct a new fixed-point expression e 0 of alternation-depth 2 and size O(r \Delta jej). Expression e 0 is equivalent to e whenever operators are distributive and the underlying complete lattice has a co-continuous least upper b ..."
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For every fixed-point expression e of alternation-depth r, we construct a new fixed-point expression e 0 of alternation-depth 2 and size O(r \Delta jej). Expression e 0 is equivalent to e whenever operators are distributive and the underlying complete lattice has a co-continuous least upper bound. We show that our transformation is optimal not only w.r.t. alternationdepth but also w.r.t. the increase in size of the resulting expression. Keywords: fixed-point expressions, distributivity, alternation-depth, lower bounds. Mathematics Subject Classification: 68Q60, 03D70, 06D99, 68Q25 1 Introduction Fixed-Point calculus is a logical formalism based on explicit notation for inductive and coinductive definitions. It is recognized as a useful framework especially for reasoning about temporal properties of finite state systems. The role of alternation of least () and greatest () fixed-point operators as a source of a sharp expressive power for the fixed-point calculus has been rec...
