8 research outputs found
Sequential Composition in the Presence of Intermediate Termination (Extended Abstract)
The standard operational semantics of the sequential composition operator
gives rise to unbounded branching and forgetfulness when transparent process
expressions are put in sequence. Due to transparency, the correspondence
between context-free and pushdown processes fails modulo bisimilarity, and it
is not clear how to specify an always terminating half counter. We propose a
revised operational semantics for the sequential composition operator in the
context of intermediate termination. With the revised operational semantics, we
eliminate transparency, allowing us to establish a close correspondence between
context-free processes and pushdown processes. Moreover, we prove the reactive
Turing powerfulness of TCP with iteration and nesting with the revised
operational semantics for sequential composition.Comment: In Proceedings EXPRESS/SOS 2017, arXiv:1709.00049. arXiv admin note:
substantial text overlap with arXiv:1706.0840
Sequential Composition in the Presence of Intermediate Termination (Extended Abstract)
The standard operational semantics of the sequential composition operator gives rise to unbounded branching and forgetfulness when transparent process expressions are put in sequence. Due to transparency, the correspondence between context-free and pushdown processes fails modulo bisimilarity, and it is not clear how to specify an always terminating half counter. We propose a revised operational semantics for the sequential composition operator in the context of intermediate termination. With the revised operational semantics, we eliminate transparency, allowing us to establish a close correspondence between context-free processes and pushdown processes. Moreover,we prove the reactive Turing powerfulness of TCP with iteration and nesting with the revised operational semantics for sequential composition
Classification of Backward Filtrations and Factor Filtrations: Examples from Cellular Automata
We consider backward filtrations generated by processes coming from
deterministic and probabilistic cellular automata. We prove that these
filtrations are standard in the classical sense of Vershik's theory, but we
also study them from another point of view that takes into account the
measurepreserving action of the shift map, for which each sigma-algebra in the
filtrations is invariant. This initiates what we call the dynamical
classification of factor filtrations, and the examples we study show that this
classification leads to different results
Realisability for Infinitary Intuitionistic Set Theory
We introduce a realisability semantics for infinitary intuitionistic set
theory that employs Ordinal Turing Machines (OTMs) as realisers. We show that
our notion of OTM-realisability is sound with respect to certain systems of
infinitary intuitionistic logic, and that all axioms of infinitary
Kripke-Platek set theory are realised. As an application of our technique, we
show that the propositional admissible rules of (finitary) intuitionistic
Kripke-Platek set theory are exactly the admissible rules of intuitionistic
propositional logic
Computational complexity theory and the philosophy of mathematics
Computational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally. This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the P≠NP problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof