A theory of synchronous relational interfaces

S. Tripakis, B. Lickly, T.A. Henzinger, E. Lee, ACM Transactions on Programming Languages and Systems (TOPLAS) 33 (2011).

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Journal Article | Published | English

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Author
Tripakis, Stavros; Lickly, Ben; Henzinger, Thomas AIST Austria ; Lee, Edward
Department
Abstract
Compositional theories are crucial when designing large and complex systems from smaller components. In this work we propose such a theory for synchronous concurrent systems. Our approach follows so-called interface theories, which use game-theoretic interpretations of composition and refinement. These are appropriate for systems with distinct inputs and outputs, and explicit conditions on inputs that must be enforced during composition. Our interfaces model systems that execute in an infinite sequence of synchronous rounds. At each round, a contract must be satisfied. The contract is simply a relation specifying the set of valid input/output pairs. Interfaces can be composed by parallel, serial or feedback composition. A refinement relation between interfaces is defined, and shown to have two main properties: (1) it is preserved by composition, and (2) it is equivalent to substitutability, namely, the ability to replace an interface by another one in any context. Shared refinement and abstraction operators, corresponding to greatest lower and least upper bounds with respect to refinement, are also defined. Input-complete interfaces, that impose no restrictions on inputs, and deterministic interfaces, that produce a unique output for any legal input, are discussed as special cases, and an interesting duality between the two classes is exposed. A number of illustrative examples are provided, as well as algorithms to compute compositions, check refinement, and so on, for finite-state interfaces.
Publishing Year
Date Published
2011-07-01
Journal Title
ACM Transactions on Programming Languages and Systems (TOPLAS)
Volume
33
Issue
4
Article Number
14
IST-REx-ID

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Tripakis S, Lickly B, Henzinger TA, Lee E. A theory of synchronous relational interfaces. ACM Transactions on Programming Languages and Systems (TOPLAS). 2011;33(4). doi:10.1145/1985342.1985345
Tripakis, S., Lickly, B., Henzinger, T. A., & Lee, E. (2011). A theory of synchronous relational interfaces. ACM Transactions on Programming Languages and Systems (TOPLAS), 33(4). https://doi.org/10.1145/1985342.1985345
Tripakis, Stavros, Ben Lickly, Thomas A Henzinger, and Edward Lee. “A Theory of Synchronous Relational Interfaces.” ACM Transactions on Programming Languages and Systems (TOPLAS) 33, no. 4 (2011). https://doi.org/10.1145/1985342.1985345.
S. Tripakis, B. Lickly, T. A. Henzinger, and E. Lee, “A theory of synchronous relational interfaces,” ACM Transactions on Programming Languages and Systems (TOPLAS), vol. 33, no. 4, 2011.
Tripakis S, Lickly B, Henzinger TA, Lee E. 2011. A theory of synchronous relational interfaces. ACM Transactions on Programming Languages and Systems (TOPLAS). 33(4).
Tripakis, Stavros, et al. “A Theory of Synchronous Relational Interfaces.” ACM Transactions on Programming Languages and Systems (TOPLAS), vol. 33, no. 4, 14, ACM, 2011, doi:10.1145/1985342.1985345.
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