Formal Languages and TQFTs with Defects
A construction that assigns a Boolean 1D TQFT with defects to a finite state automaton was recently developed by Gustafson, Im, Kaldawy, Khovanov, and Lihn. We show that the construction is functorial with respect to the category of finite state automata with transducers as morphisms. Certain classes of subregular languages correspond to additional cohomological structures on the associated TQFTs. We also show that the construction generalizes to context-free grammars through a categorical version of the Chomsky-Sch\"utzenberger representation theorem, due to Melli\`es and Zeilberger. The corresponding TQFTs are then described as morphisms of colored operads on an operad of cobordisms with defects.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Towards a unified framework for programming paradigms: A systematic review of classification formalisms and methodological foundations
The rise of multi-paradigm languages challenges traditional classification methods, leading to practical software engineering issues like interoperability defects. This systematic literature review (SLR) maps the formal …
Conformal Defects in Neural Network Field Theories
Neural Network Field Theories (NN-FTs) represent a novel construction of arbitrary field theories, including those of conformal fields, through the specification of the network architecture and prior distribution for the…
Automatic White-Box Testing of First-Order Logic Ontologies
Formal ontologies are axiomatizations in a logic-based formalism. The development of formal ontologies, and their important role in the Semantic Web area, is generating considerable research on the use of automated reaso…
Faults in Our Formal Benchmarking: Dataset Defects and Evaluation Failures in Lean Theorem Proving
Benchmarks for LLM-assisted theorem proving in Lean are often treated as intrinsically reliable because every solved instance comes with a machine-checked proof. However, the kernel only checks that a proof establishes a…
The Platform for non-metallic pipes defects recognition. Design and Implementation
This paper describes a prototype software and hardware platform to provide support to field operators during the inspection of surface defects of non-metallic pipes. Inspection is carried out by video filming defects cre…