The Correspondence Between Monotonic Many Sorted Signatures and Well - Founded Graphs . Part I
نویسنده
چکیده
We prove a number of auxiliary facts about graphs, mainly about vertex sequences of chains and oriented chains. Then we define a graph to be well-founded if for each vertex in the graph the length of oriented chains ending at the vertex is bounded. A wellfounded graph does not have directed cycles or infinite descending chains. In the second part of the article we prove some auxiliary facts about free algebras and locally-finite algebras.
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The Correspondence Between Monotonic Many Sorted Signatures and Well - Founded Graphs . Part I 1 Czes law
We prove a number of auxiliary facts about graphs, mainly about vertex sequences of chains and oriented chains. Then we define a graph to be well-founded if for each vertex in the graph the length of oriented chains ending at the vertex is bounded. A well-founded graph does not have directed cycles or infinite descending chains. In the second part of the article we prove some auxiliary facts ab...
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The graph induced by a many sorted signature is defined as follows: the vertices are the symbols of sorts, and if a sort s is an argument of an operation with result sort t, then a directed edge [s, t] is in the graph. The key lemma states relationship between the depth of elements of a free many sorted algebra over a signature and the length of directed chains in the graph induced by the signa...
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The graph induced by a many sorted signature is defined as follows: the vertices are the symbols of sorts, and if a sort s is an argument of an operation with result sort t, then a directed edge [s, t] is in the graph. The key lemma states relationship between the depth of elements of a free many sorted algebra over a signature and the length of directed chains in the graph induced by the signa...
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This article is the second in a series of four articles (started with [19] and continued in [18], [20]) about modelling circuits by many sorted algebras. First, we introduce some additional terminology for many sorted signatures. The vertices of such signatures are divided into input vertices and inner vertices. A many sorted signature is called circuit like if each sort is a result sort of at ...
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This article is the second in a series of four articles (started with [20] and continued in [19,18]) about modelling circuits by many sorted algebras. First, we introduce some additional terminology for many sorted signatures. The vertices of such signatures are divided into input vertices and inner vertices. A many sorted signature is called circuit like if each sort is a result sort of at mos...
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