Representation of Partial Traces

Representation of Partial Traces

The notion of trace in a monoidal category has been introduced to give a categorical account of a situation occurring in very different settings: linear algebra, topology, knot theory, proof theory. . . with the trace operation understood as a feedback operation. Partially traced categories were later introduced to account for cases where the trace is not always defined, and it was shown that p...

Partial Data Traces: Efficient Generation and Representation

Binary manipulation techniques are increasing in popularity. They support program transformations tailored toward certain program inputs, and these transformations have been shown to yield performance gains beyond the scope of static code optimizations without profile-directed feedback. They even deliver moderate gains in the presence of profile-guided optimizations. In addition, transformation...

Partial Commutation and Traces

Representation and Implementation of CSP and VCR Traces

Communicating Sequential Processes (CSP) was developed around a formal algebra of processes and a semantics based on traces (and failures and divergences). A trace is a record of the events engaged in by a process. Several programming languages use, or have libraries to use, CSP mechanisms to manage their concurrency. Most of these lack the facility to record the trace of a program. A standard ...

On the Physical Interpretation of Partial Traces: Two Nonstandard Viewpoints

Mixed states are introduced in physics in order to express our ignorance about the actual state of a physical system and are represented in standard quantum mechanics (QM) by density operators. Such operators also appear if one considers a (pure) entangled state of a compound system Ω and performs partial traces on the projection operator representing it. Yet, they do not represent mixed states...