## Algebra of Flownomials; Part 1: Binary Flownomials; Basic Theory

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@MISC{Stefanescu_algebraof,

author = {Gheorghe Stefanescu},

title = {Algebra of Flownomials; Part 1: Binary Flownomials; Basic Theory},

year = {}

}

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### Abstract

' morphism for connecting flowgraphs are used in [CaU82] and in all of our subsequent papers on flowchart schemes and flownomials, see [Ste87a, Ste87b, CaS88a, CaS90a, CaS92]. This chapter folows Chapter B, sec. 3--6 of [Ste91]. The main result is based on a series of papers dealing with the algebraization of flowchart schemes, including [CaU82, BlEs85, Ste86/90, Bar87a, CaS88a, CaS90b]. With different sets of operators various algebras for flowgraphs appear in [Mil79, Parr87, CaS90b, CaS88b]. In the classical algebraic calculus for regular languages it is often the case that certain abstract semirings are used instead of the Boolean f0; 1g semiring, e.g. by using formal series with such coefficients. 5 This property is similar to the universal property of the polynomials over a ring. Chapter 6 Graph isomorphism with various constants In this chapter we extend the axiomatistion for flowgraphs modulo isomorphism to the case where more constants for generating relations are present i...

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Citation Context ... used, then the possibility to get an algebra for flowgraphs themselves is lost.] The normal form flownomial expressions are introduced in [Ste86, Ste86/90]. In the general form they are presented in =-=[CaS90a]-=-. The presentation from this chapter follows the one in Chapter B, sec. 1--2 of [Ste91]. Chapter5 Algebra of flowgraphs (aff--flow) In this chapter we justify our claim that aff-flownomials represent ... |

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diagrams and 2-dimensional rewriting
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Citation Context ...MC Ss. 2 2.7 Short comments and references The results of this chapter are based on [CaS91]. The presentation we have given follows the slightly improved version presented in Chapter A of [Ste91]. In =-=[Laf92]-=- a confluent and terminating rewriting system is given for affi-terms (functions) . Chapter 3 Critical acyclic structures (strong xy-ssmc's) In this chapter we introduce three critical structures that... |

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Citation Context ...he dual one. 2 C R 7 OWGR V OURS# G R C S 0 7.4 Short comments and references This chapter is a technical one. It is based on Chapter C of [Ste91]. The enzymatic rule via general functions is used in =-=[ArM80]-=- under the name `functoriality rule', a name which was also used in our previous papers. In an implicit way the enzymatic rule for functions appear in the axiomatization of iteration theories in [Esi8... |

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Citation Context ...c \Phi? d ) (I a \Phi? b ) \Delta f \Delta (? c \Phi I d ) (? a \Phi I b ) \Delta f \Delta (I c \Phi? d ) (? a \Phi I b ) \Delta f \Delta (? c \Phi I d ) ! : We mention here the following result (see =-=[Elg76a]-=-). Let B be a matrix theory over (IN# +# 0). On the set B(1# 1) we introduce the operations f [ g =s1 \Delta (f \Phi g) \Delta 1# f \Delta g = f \Delta g# 0=? 1 \Delta? 1# and 1=I 1 : So we get a semi... |

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Citation Context ...n this first part we present the kernel of the calculus of binary flownomials. Complete proofs are given for all the results, except for some commuting lemmas used in Chapter 11 which may be found in =-=[Ste87b]-=- and for which I have no better proofs. A few references are included. More refernces and connections with related topics, applications, particular models and equivalent presentations for various alge... |