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Minimal realization of machines in closed categories

1972
*
Bulletin of the American Mathematical Society
*

*Functors*are written after their arguments. AM S 1970 subject classifications. Primary 18D10, 18B20. ... There has been recent interest in extending automaton theory to encompass aspects of

*machine*, language, and control theories [1], [2]. ... Moreover, affine

*machines*are richer in (loosely speaking) allowing multiplications between inputs and

*states*. This type of

*machine*and its minimal realization theory seem to be new. ...

##
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Page 1617 of Mathematical Reviews Vol. 34, Issue 6
[page]

1967
*
Mathematical Reviews
*

E.
partition of equivalence classes of strongly connected | Stearns, Algebraic structure theory of sequential

*machines*,*states*. ... Ifa*machine*minimization; (4)*State*identification experi- | natural reflector of @ is distinguishable then @ is trans- ments ; (5)*Machine*identification experiments ; (6) Finite- | parent. oy is thus ...##
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Universal realization

1979
*
Journal of computer and system sciences (Print)
*

For a given input-process X: K + K the categories Mach(X) of

doi:10.1016/0022-0000(79)90005-9
fatcat:3nmqttkfnnhdrloq6qgpfyjqmi
*machines*and Beh(X) of behaviors are constructed, also a*functor*E: Mach(X) + Beh(X) which assigns to each*machine*its behavior. ... A consequence is a characterization of minimal realization*functors*: a result similar to those arrived at by Goguen for*machines*in closed categories. ... [7] for*machines*in closed categories. Results in [13] on*state*-behavior*machines*are also extended to input-process*machines*. ...##
###
Limits and colimits in a category of lenses
[article]

2021
*
arXiv
*
pre-print

Example 5.7 (Pullbacks as independent components of a

arXiv:2105.05422v1
fatcat:s3xamtpmhzhujljprw4krbasom
*state**machine*). Consider two*state*-*machines*A and C over the same interface B, as lenses A B and C B. ... The imported pullback lens A × B C B models a*state*-*machine*where the*states*are pairs (a ∈ A, c ∈ C); it can be viewed as a*state*-*machine*with two independent components A and C, which concurrently update ...##
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Theoretical Computer Science for the Working Category Theorist
[article]

2017
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arXiv
*
pre-print

Surprisingly, many interesting theorems and concepts of theoretical computer science are easy consequences of functoriality and composition when you look at the right categories and

arXiv:1710.03090v1
fatcat:4prsflvgqnbqpliloqrywifgda
*functors*connecting ... Figure 2 : 2 A Turing*Machine*processes at one time. The set of*states*is the product of the two sets of*states*. ... After the T*machine*halts, the*machine*will go to the start*state*of the T*machine*. If the T*machine*does not halt, the T*machine*never even begins. ...##
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Dynamical Systems and Sheaves
[article]

2019
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arXiv
*
pre-print

Moore

arXiv:1609.08086v4
fatcat:nzdzfhzb5bddrlaoted2p7gsee
*machines*). Additionally, morphisms between the different types of systems allow their translation in a common framework. ... The fundamental categorical tools used here include lax monoidal*functors*, which provide a language of compositionality, as well as sheaf theory, which flexibly captures the crucial notion of time. ... of*state*to match. ...##
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Machines in a category

1980
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Journal of Pure and Applied Algebra
*

Willsky, Finite-

doi:10.1016/0022-4049(80)90090-0
fatcat:eylerllivff7holujcxxug6j74
*state*homomorphic sequential*machines*, IEEE Trans. .Aut. Intertwined recursion, tree rransformattons and linear systems, (1969) 589-606. [I21 E.S. ... for*machines*in a hyper- doctrine, ...##
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Generalizing determinization from automata to coalgebras

2013
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Logical Methods in Computer Science
*

Many types of transition systems and their equivalences can be captured by a

doi:10.2168/lmcs-9(1:9)2013
fatcat:3i3h4rre6bcvblbpcke4rr6cfq
*functor*F. ... In this paper, we lift the powerset construction from automata to the more general framework of coalgebras with structured*state*spaces. ... Analogously to our approach, each λ-*machine*induces an "implicit λ-*machine*" having T X as*state*space. ...##
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Concurrent Separation Logic Meets Template Games
[article]

2020
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arXiv
*
pre-print

The second internal

arXiv:2005.04453v1
fatcat:npkbdkzwjnfvnf3t6jbmu25xr4
*functor*u L forgets the memory from a*machine**state*in order to obtain the corresponding lock*state*. ... The*machine*model of separated*states*• Sep In contrast to the*stateful*and the stateless*machine*models • S and • L , which are one-player games, the*machine*model of separated*states*involves two players ...##
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Natural state transformations

1975
*
Journal of computer and system sciences (Print)
*

., maps that change the underlying structure, rather than sequential

doi:10.1016/s0022-0000(75)80045-6
fatcat:lgjargqawvel3evuh7n73sxisa
*machines*, are emphasized and natural*state*transformations are defined as certain generalized morphisms of monads. ... On this basis, a duality theory for direct and inverse*state*transformations is developed, which lays bare the relationship between the two models of finite*state*(tree) transformations mentioned above ... If in the definition of an inverse*state*transformation of the form QT-:+ TQ we replace the*state**functor*with the input process X and T with a "nondeterministic*functor*" (like the power set*functor*) we ...##
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Towards Modular Compilers for Effects
[chapter]

2012
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Lecture Notes in Computer Science
*

However, there is another potential factorisation that has received comparatively little attention: the treatment of separate language features, such as mutable

doi:10.1007/978-3-642-32037-8_4
fatcat:6yp6h457tffahittobkej3txou
*state*, input/output, exceptions, concurrency ... We execute the resulting Code on a virtual*machine*that operates using a Stack: The correctness of the compiler can now be captured by*stating*that the result of evaluating an expression is the same as ... Using the notion of subtyping, we can define an injection function, Note the constraints*stating*that f must have the appropriate signature*functor*as a subtype; for example, in the case of val, f must ...##
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Towards Trace Metrics via Functor Lifting

2015
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Conference on Algebra and Coalgebra in Computer Science
*

The trace distance between two

doi:10.4230/lipics.calco.2015.35
dblp:conf/calco/BaldanBK015
fatcat:q737653gurd3lnw7go6u5uuzie
*states*of the original coalgebra is the distance between their images in the determinized coalgebra through the unit of the monad. ... First, we generalize a technique for systematically lifting*functors*from the category Set of sets to the category PMet of pseudometric spaces, by identifying conditions under which also natural transformations ... In the first case, T is the powerset monad P fin and F is the*machine**functor*M 2 = 2 × _ A , while in the second case T is the distribution monad D and F is the*machine**functor*M [0,1] = [0, 1] × _ A ...##
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Interaction and observation, categorically

2011
*
Electronic Proceedings in Theoretical Computer Science
*

While the

doi:10.4204/eptcs.59.3
fatcat:zwqn23tttfa47ic2ccdlo4bzee
*machine*is running, the observer performs its experiments, and observes some side-effects. The*machines*reaches a new*state*. ... That is, a current*state*of the*machine*is defined, and the*machine*has an underlying operational semantics, which is what the*machine*really does, independently from what the observer sees. ...##
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View Consistency in Software Development
[chapter]

2004
*
Lecture Notes in Computer Science
*

The model

doi:10.1007/978-3-540-24626-8_24
fatcat:ckc4hrzmw5fcxnbszfmj6j5vru
*functor*Mod Mach maps a*state**machine*diagram to the class of algebras with transitions for the*machines*in the diagram. ... B.5*State**Machine*Viewpoint Syntax. A*state**machine*diagram C, µ is given by a set of classes C and a mapping µ of classes to*machines*. ...##
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Adjoint machines, state-behavior machines, and duality

1975
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Journal of Pure and Applied Algebra
*

There exist

doi:10.1016/0022-4049(75)90028-6
fatcat:mzrhit5zqra6ve6xxlbp6xizoa
*state*-behavior*machines*which are not adjoint (but not in Set). ... Adjoint*machines*(*machines*with adjoint input processes) provide the first integration of classical sequential*machines*(the only*state*-behavior*machines*in the category, Set, of sets), metric*machines*... Setting '23 = DynfX) and d =%' , we have for U the forgetful*functor*that LU = X@ and RU = X@ so that we have established 4.4. A~jointne~ principle for*state*-behavior*machines*. ...
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