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Minimal realization of machines in closed categories

J. A. Goguen
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.  ... 
doi:10.1090/s0002-9904-1972-13032-5 fatcat:wcwr24jsp5fwbo6uwqwiusgbha

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  ... 

Universal realization

G. Naudé
1979 Journal of computer and system sciences (Print)  
For a given input-process X: K + K the categories Mach(X) of 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.  ... 
doi:10.1016/0022-0000(79)90005-9 fatcat:3nmqttkfnnhdrloq6qgpfyjqmi

Limits and colimits in a category of lenses [article]

Emma Chollet, Bryce Clarke, Michael Johnson, Maurine Songa, Vincent Wang, Gioele Zardini
2021 arXiv   pre-print
Example 5.7 (Pullbacks as independent components of a 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  ... 
arXiv:2105.05422v1 fatcat:s3xamtpmhzhujljprw4krbasom

Theoretical Computer Science for the Working Category Theorist [article]

Noson S. Yanofsky
2017 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 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.  ... 
arXiv:1710.03090v1 fatcat:4prsflvgqnbqpliloqrywifgda

Dynamical Systems and Sheaves [article]

Patrick Schultz and David I. Spivak and Christina Vasilakopoulou
2019 arXiv   pre-print
Moore 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.  ... 
arXiv:1609.08086v4 fatcat:nzdzfhzb5bddrlaoted2p7gsee

Machines in a category

Michael A. Arbib, Ernest G. Manes
1980 Journal of Pure and Applied Algebra  
Willsky, Finite-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,  ... 
doi:10.1016/0022-4049(80)90090-0 fatcat:eylerllivff7holujcxxug6j74

Generalizing determinization from automata to coalgebras

Alexandra Silva, Filippo Bonchi, Marcello Bonsangue, Jan Rutten, Prakash Panangaden
2013 Logical Methods in Computer Science  
Many types of transition systems and their equivalences can be captured by a 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.  ... 
doi:10.2168/lmcs-9(1:9)2013 fatcat:3i3h4rre6bcvblbpcke4rr6cfq

Concurrent Separation Logic Meets Template Games [article]

Paul-André Melliès, Léo Stefanesco
2020 arXiv   pre-print
The second internal 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  ... 
arXiv:2005.04453v1 fatcat:npkbdkzwjnfvnf3t6jbmu25xr4

Natural state transformations

Suad Alagić
1975 Journal of computer and system sciences (Print)  
., maps that change the underlying structure, rather than sequential 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  ... 
doi:10.1016/s0022-0000(75)80045-6 fatcat:lgjargqawvel3evuh7n73sxisa

Towards Modular Compilers for Effects [chapter]

Laurence E. Day, Graham Hutton
2012 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 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  ... 
doi:10.1007/978-3-642-32037-8_4 fatcat:6yp6h457tffahittobkej3txou

Towards Trace Metrics via Functor Lifting

Paolo Baldan, Filippo Bonchi, Henning Kerstan, Barbara König, Marc Herbstritt
2015 Conference on Algebra and Coalgebra in Computer Science  
The trace distance between two 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  ... 
doi:10.4230/lipics.calco.2015.35 dblp:conf/calco/BaldanBK015 fatcat:q737653gurd3lnw7go6u5uuzie

Interaction and observation, categorically

Vincenzo Ciancia
2011 Electronic Proceedings in Theoretical Computer Science  
While the 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.  ... 
doi:10.4204/eptcs.59.3 fatcat:zwqn23tttfa47ic2ccdlo4bzee

View Consistency in Software Development [chapter]

Martin Wirsing, Alexander Knapp
2004 Lecture Notes in Computer Science  
The model 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.  ... 
doi:10.1007/978-3-540-24626-8_24 fatcat:ckc4hrzmw5fcxnbszfmj6j5vru

Adjoint machines, state-behavior machines, and duality

Michael A. Arbib, Ernest G. Manes
1975 Journal of Pure and Applied Algebra  
There exist 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.  ... 
doi:10.1016/0022-4049(75)90028-6 fatcat:mzrhit5zqra6ve6xxlbp6xizoa
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