Introduction to higher order categorical logic
Introduction to higher order categorical logic
Algebraic approaches to program semantics
Algebraic approaches to program semantics
Topology via logic
Handbook of logic in computer science (vol. 3): semantic structures
Handbook of logic in computer science (vol. 3): semantic structures
Basic proof theory
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Domains and lambda-calculi
A new kind of science
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Basic techniques for two-way finite automata
Proceedings of the LITP Spring School on Theoretical Computer Science: Formal Properties of Finite Automata and Applications
Geometry of interaction 2: deadlock-free algorithms
COLOG '88 Proceedings of the International Conference on Computer Logic
Domains for Denotational Semantics
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Retracting Some Paths in Process Algebra
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
On the power of quantum finite state automata
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
A categorical framework for finite state machines
Mathematical Structures in Computer Science
Geometry of Interaction and linear combinatory algebras
Mathematical Structures in Computer Science
A categorical model for the geometry of interaction
Theoretical Computer Science - Automata, languages and programming: Logic and semantics (ICALP-B 2004)
Physical systems as constructive logics
UC'06 Proceedings of the 5th international conference on Unconventional Computation
Quantum circuit oracles for Abstract Machine computations
Theoretical Computer Science
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Using simple systems with a notion of discrete deterministic evolution over time, we study discrete causality via tools from theoretical computer science and logic. We consider the set of all representations (i.e. partial descriptions) of such systems, from algebraic, domain-theoretic, and categorical viewpoints. The order theory introduced, is based in the notion of comparing high-level and low-level descriptions of the same system. This is shown to give a Complete Partial Order where the down-closure of each element is a locale. This partial order has a very close connection to a categorical construction known as the 'particle-style' trace, via analogues of domain-theoretic equations. Thus, the trace may be thought of as the computation of suprema in this partial order. As a sample application, we show how to construct algebraic models of space-bounded Turing machines in these terms, and derive compositionality from the abstract properties of the trace.