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==Finite Automata== ...e will study the languages belonging to certain automata. <!-- and not the automata. would things like state complexity fit here? --> ...

Mitchell, B.: 1965, ''Theory of Categories'' , Academic Press: London. Bibliography of Category Theory and Algebraic Topology. ...

[http://planetmath.org/encyclopedia/HomotopyCategory2.html Homotopy Theory] for groupoids that leads to analogies between groupoids and spaces or [[.. ...aton/|state spaces]] are semigroups. Interestingly, the category of finite automata, just like <math>G_{pd}</math> is also ''cartesian closed'' ; ...

{{nav3|Wikiversity|Wikiversity:School of Computer Science|Wikiversity:Theory}} ...es of language families defined in a wide variety of ways. Formal language theory is concerned with the purely syntactical aspects, rather than a semantics o ...

...ding quantum logics, [[../LM_nLogicAlgebra/|many-valued logics]], automata theory), and so on, to obtain physically relevant results --that are often numeric *[[../PreciseIdea/|concepts]]: UTM, [[../QuantumComputers/|quantum automata]] concepts ...

...rAlgebra4/|operators]] #[[../CosmologicalConstant/|Algebraic Quantum Field Theory]] #[[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topo #Conformal Map theory (CMT) ...

...Salomaa's book<ref name="Salomaa">Arto Salomaa, Jewels in Formal Language Theory, Computer Science Press 1981</ref>. ...or Symmetry and Implicitness, p. 53: interesting connection between finite automata and D0L systems --> ...

...utomata [[../GroupoidHomomorphism2/|topological groupoid]] spaces of reset automata [[../RModule/|modules]] *Generalized [[../QuantumComputers/|quantum automata]] ...

...extension of both Rashevsky's [[../TheoryOfOrganismicSets/|organismic set theory]] and Robert Rosen's Metabolic-Replication Systems Set-Categorical approach ...ical Model of Genetic Activities in \L ukasiewicz Algebras: The Non-linear Theory. ''Bulletin of Mathematical Biophysics'' , '''39''' : 249-258. ...

'''Remark.''' Other definitions of quantum automata and quantum computations have also been reported that are ...ref name='ICB71a'/> and <ref name='ICB71b'/> as generalized, probabilistic automata with quantum state spaces. Their next-state [[../Bijective/|functions]] ope ...

...<math>S_0</math> in the simpler, Rashevsky's [[../TheoryOfOrganismicSets/|theory of organismic sets]]. ...ographyOfCategoryTheory.html [14] to [34] in the "bibliography of category theory and algebraic topology"] ...

...hematicalFoundationsOfQuantumTheories/|mathematical foundations of quantum theory]] in physics was also closely involved with the design and building of the #Accelerator design and operational theory ...

...nse as subcategories of the category of [[../AAT/|sequential machines]] or automata, in a somewhat ironical vindication of the French philosopher Descartes' su ...tomaton]], with the possible exception of ''[[../QuantumComputers/|quantum automata]]''. Rosen's relational approach to Biology is an extension and amplificati ...

The ''theory of organismic sets and their abstract [[../Bijective/|relations]]'', (''[[. ...quivalence/|system's]] organization. Therefore, Rashevsky's organismic set theory is part of [[../SystemsBiology/|abstract relational biology]]. ''First orde ...

is a subcategory of the [[../AAT/|category of automata]] (or [[../AAT/|sequential machines]]), <math>\mathcal{S}_{[M,A]}</math> (< ...obertRosen/|Robert Rosen]] developed with several coworkers the MR-systems theory and its applications ...

Towards a Unitary Theory of Systems. ''Bulletin of Mathematical Biophysics'' '''30''' , 148-159. ...ical Model of Genetic Activities in \L ukasiewicz Algebras: The Non-linear Theory. ''Bulletin of Mathematical Biology'' , '''39''' : 249-258. ...

* [[Relation theory]] * [[Truth theory]] ...

...utomata [[../GroupoidHomomorphism2/|topological groupoid]] spaces of reset automata [[../RModule/|modules]] *Generalized [[../QuantumComputers/|quantum automata]] ...

...of the axioms in ETAS- a natural extension of Lawvere's <math>elementary\; theory\; of \; abstract \; categories</math> ([[../ETACAxioms/|ETAC]]) to [[../Abe References [14] to [34] in the "bibliography of category theory and algebraic topology" ...

* [[Relation theory]] * [[Truth theory]] ...