결합법칙 만족
...
...
//eom
semigroup with identity
semigroup with identity
//wpko
항등원,identity_element을 갖는
결합법칙,associativity을 따르는
이항연산,binary_operation을 갖춘 대수구조,algebraic_structure.
항등원,identity_element을 갖는
결합법칙,associativity을 따르는
이항연산,binary_operation을 갖춘 대수구조,algebraic_structure.
i.e.
"추상대수학에서 모노이드는 항등원,identity_element을 갖는, 결합법칙,associativity을 따르는 이항연산,binary_operation을 갖춘 대수구조,algebraic_structure이다. 군,group의 정의에서 역원,inverse_element의 존재를 생략하거나, 반군,semigroup(semigroup)의 정의에서 항등원,identity_element의 존재를 추가하여 얻는다."
"추상대수학에서 모노이드는 항등원,identity_element을 갖는, 결합법칙,associativity을 따르는 이항연산,binary_operation을 갖춘 대수구조,algebraic_structure이다. 군,group의 정의에서 역원,inverse_element의 존재를 생략하거나, 반군,semigroup(semigroup)의 정의에서 항등원,identity_element의 존재를 추가하여 얻는다."
1.2. free monoid ¶
free_monoid= https://en.wiktionary.org/wiki/free_monoid
"(algebra) A monoid whose underlying_set is the Kleene_closure of some set of generator제너레이터,generators, and whose operator연산자,operator is concatenationconcatenation."
underlying_set is the Kleene_closure of some set of generator제너레이터,generators, and whose operator연산자,operator is concatenationconcatenation."
Free_monoid= https://en.wikipedia.org/wiki/Free_monoid
https://encyclopediaofmath.org/wiki/Free_semi-group
단어,word
알파벳,alphabet
문자열,string
(Redirected from Free monoid)
REL/MKL:단어,word
알파벳,alphabet
문자열,string
}
1.4. monoidal category ¶
monoidal_category =,monoidal_category . monoidal_category
monoidal_category
forkto 모노이드범주,monoidal_category
범주,category
monoidal_categoryforkto 모노이드범주,monoidal_category
범주,category
1.5. submonoid ¶
submonoid
=,submonoid . submonoid
부분 모노이드
부분모노이드,submonoid
https://mathworld.wolfram.com/Submonoid.html
submonoid
submonoid
=,submonoid . submonoid
부분 모노이드
부분모노이드,submonoid
https://mathworld.wolfram.com/Submonoid.html
submonoidsubmonoid1.7. syntactic monoid ¶
syntactic_monoid x 2024-03} // syntactic monoid ....
syntactic monoid 
syntactic monoid syntactic monoid1.8. trace monoid ¶
trace_monoid =,trace_monoid . trace_monoid
trace_monoid x (2023-08-17)https://en.wikipedia.org/wiki/Trace_monoid
trace는 문자열,string. =,trace . trace { Sub: trace_cache =,trace_cache =,trace_cache . trace_cache
{
trace cache{
(we)"In 컴퓨터구조,computer_architecture,
a trace cache or execution trace cache
is a specialized instruction_cache { instruction_cacheinstruction_cache }
which stores the dynamic stream of 명령어,instructions known as trace.
.....
A trace processor is an architecture designed around the trace cache and processes the instructions at trace level granularity.
The formal mathematical theory of traces is described by trace monoids."
a trace cache or execution trace cache
is a specialized instruction_cache { instruction_cache
instruction_cache }which stores the dynamic stream of 명령어,instructions known as trace.
.....
A trace processor is an architecture designed around the trace cache and processes the instructions at trace level granularity.
The formal mathematical theory of traces is described by trace monoids."
trace_cache
execution trace cache
execution_trace_cache
instruction cache
instruction_cache
trace processor
trace_processor
trace monoid
trace_monoid
명령어,instruction 실행,execution 트레이스,trace? 캐시,cache 프로세서,processor 모노이드,monoid
https://en.wikipedia.org/wiki/Trace_cache
}
기타 trace / tracing 에 대해 더: =,trace =,tracing .
https://ko.wikipedia.org/wiki/트레이싱
Tracing_(software)
= https://en.wikipedia.org/wiki/Tracing_(software)
= https://en.wikipedia.org/wiki/Tracing_(software)
cmp event_logging
Tracing_(software)= https://en.wikipedia.org/wiki/Tracing_(software)
= https://en.wikipedia.org/wiki/Tracing_(software)
https://en.wikipedia.org/wiki/Trace_theory
DTrace (FreeBSD and SmartOS) { https://ko.wikipedia.org/wiki/DTrace https://en.wikipedia.org/wiki/DTracedtrace }
ftrace (Linux_kernel) https://en.wikipedia.org/wiki/Ftrace
WPP(?) (Windows) https://en.wikipedia.org/wiki/Windows_software_trace_preprocessor
그리고 추가로 비슷한것들, via https://en.wikipedia.org/wiki/DTrace#See_also :
eBPF (Linux_kernel) {
ktrace }
ltrace (Linux, userland application이 shared_library =,shared_library . shared_library { shared_library = shared_object .... https://en.wikipedia.org/wiki/Shared_library }호출하는 것을 보여주는 debugging utility) { (동적로딩 dynamic_loading 동적링킹 dynamic_linking linked to: https://ko.wikipedia.org/wiki/동적_적재 https://en.wikipedia.org/wiki/Dynamic_loading https://en.wikipedia.org/wiki/Dynamic_linker (Redirected fromDynamic_linking) )시스템을 hooking ... shim 을 삽입 ... static_linking(rel static_library = statically-linked_library .. linked to: https://ko.wikipedia.org/wiki/정적_라이브러리 https://en.wikipedia.org/wiki/Static_library ) 된 호출들은 trace할 수 없음. ... https://ko.wikipedia.org/wiki/Ltrace https://en.wikipedia.org/wiki/Ltrace }
strace (Linux, system_call 및 signal 을 모니터링하는 debugging utility) https://en.wikipedia.org/wiki/Strace
LTT Linux Trace Toolkit (LTT) { https://en.wikipedia.org/wiki/Linux_Trace_Toolkit }
and
LTTng Linux Trace Toolkit Next Generation (LTTng) {https://en.wikipedia.org/wiki/LTTngLTTng }
SystemTap (Linux_kernel tracing tool) { SystemTap (stap) scripting_language and tool for dynamic instrumentation =,instrumentation . instrumentation { instrumentation https://ko.wikipedia.org/wiki/인스트루먼테이션Instrumentation_(computer_programming) = https://en.wikipedia.org/wiki/Instrumentation_(computer_programming) = https://en.wikipedia.org/wiki/Instrumentation_(computer_programming) trace instrumentation } https://ko.wikipedia.org/wiki/SystemTap https://en.wikipedia.org/wiki/SystemTap SystemTap }
truss
ProbeVue (IBM AIX lightweight dynamic tracing environment) { https://en.wikipedia.org/wiki/ProbeVueProbeVue }
....
}
........ADDHERE.........
DTrace (FreeBSD and SmartOS) { https://ko.wikipedia.org/wiki/DTrace https://en.wikipedia.org/wiki/DTrace
dtrace }ftrace (Linux_kernel) https://en.wikipedia.org/wiki/Ftrace
WPP(?) (Windows) https://en.wikipedia.org/wiki/Windows_software_trace_preprocessor
그리고 추가로 비슷한것들, via https://en.wikipedia.org/wiki/DTrace#See_also :
eBPF (Linux_kernel) {
BPF : Berkeley_Packet_Filter { Berkeley Packet Filter (BPF) https://en.wikipedia.org/wiki/Berkeley_Packet_Filter }
https://en.wikipedia.org/wiki/EBPF ...eBPF eBPF eBPF }
ktrace (BSD and macOS, kernel-program interaction tracer) { ktrace이게 생성한 것은 kdump로 읽는다. https://ko.wikipedia.org/wiki/Ktrace https://en.wikipedia.org/wiki/Ktrace https://en.wikipedia.org/wiki/EBPF ...
eBPF eBPF eBPF }ktrace }ltrace (Linux, userland application이 shared_library =,shared_library . shared_library { shared_library = shared_object .... https://en.wikipedia.org/wiki/Shared_library }호출하는 것을 보여주는 debugging utility) { (동적로딩 dynamic_loading 동적링킹 dynamic_linking linked to: https://ko.wikipedia.org/wiki/동적_적재 https://en.wikipedia.org/wiki/Dynamic_loading https://en.wikipedia.org/wiki/Dynamic_linker (Redirected from
Dynamic_linking) )시스템을 hooking ... shim 을 삽입 ... static_linking(rel static_library = statically-linked_library .. linked to: https://ko.wikipedia.org/wiki/정적_라이브러리 https://en.wikipedia.org/wiki/Static_library ) 된 호출들은 trace할 수 없음. ... https://ko.wikipedia.org/wiki/Ltrace https://en.wikipedia.org/wiki/Ltrace }strace (Linux, system_call 및 signal 을 모니터링하는 debugging utility) https://en.wikipedia.org/wiki/Strace
LTT Linux Trace Toolkit (LTT) { https://en.wikipedia.org/wiki/Linux_Trace_Toolkit }
and
LTTng Linux Trace Toolkit Next Generation (LTTng) {https://en.wikipedia.org/wiki/LTTng
LTTng }SystemTap (Linux_kernel tracing tool) { SystemTap (stap) scripting_language and tool for dynamic instrumentation =,instrumentation . instrumentation { instrumentation https://ko.wikipedia.org/wiki/인스트루먼테이션
Instrumentation_(computer_programming) = https://en.wikipedia.org/wiki/Instrumentation_(computer_programming) = https://en.wikipedia.org/wiki/Instrumentation_(computer_programming) trace instrumentation } https://ko.wikipedia.org/wiki/SystemTap https://en.wikipedia.org/wiki/SystemTap SystemTap }truss
ProbeVue (IBM AIX lightweight dynamic tracing environment) { https://en.wikipedia.org/wiki/ProbeVue
ProbeVue }....
}
........ADDHERE.........
6. tmp video en ¶
Monoids | Group theory episode 1 - YouTube / All Angles
https://www.youtube.com/watch?v=dYN8Q4Ms5U4
{
easy. 22m.
https://www.youtube.com/watch?v=dYN8Q4Ms5U4
{
easy. 22m.
군론,group_theory series에서 첫번째 ep인 듯
가장 간단한 예는 (set of natural numbers) with (addition).
$\displaystyle N$ 은 closed under addition.
$\displaystyle (N,+)$
여기서 $\displaystyle N=\{0,1,2,3,4,\ldots\}$$\displaystyle N$ 은 closed under addition.
neutral/identity element 포함. 저것은 $\displaystyle +$ 에 대한 효과가 없음(no effect).
$\displaystyle +$ 은 binary operation.associative. $\displaystyle (a+b)+c = a+(b+c)$
또 다른 예는 string(원소에 empty string 포함, 연산은 concatenation)- strings are closed under concatenation. ✔️
- concatenation is associative. (ab)c=a(bc). ✔️
- empty string is neutral/identity element. ✔️
원 색칠(파랑 노랑)으로 비유하는데 .... 왜 명령어,instruction들로 이루어진 subroutine의 실행,execution이 monoid에 비유되는지 알 수 있다. (semicolon ; is binary operation)
입출력,IO도 마찬가지.
for_loop 도.
암튼 PL의 스테이트먼트,statements' 대수적algebraic 추상화,abstraction에 쓰임.
입출력,IO도 마찬가지.
for_loop 도.
암튼 PL의 스테이트먼트,statements' 대수적algebraic 추상화,abstraction에 쓰임.
}
7. Inter ¶
https://everything2.com/title/monoid
{
번역at2023-09-26
Monoid는 거의 군,group이다. 유일하게 군의 조건을 만족하지 못하는 것이 그 안의 모든 원소,element가 인버스,inverse(역,inverse 역원,inverse_element?)을 가질 필요가 없다는 점이다.
모노이드는 항등원,identity_element을 가진다(이 특징을 semigroup과 대조해 보라.) - TBW
Contrast: semigroup
}
{
번역at2023-09-26
Monoid는 거의 군,group이다. 유일하게 군의 조건을 만족하지 못하는 것이 그 안의 모든 원소,element가 인버스,inverse(역,inverse 역원,inverse_element?)을 가질 필요가 없다는 점이다.
모노이드는 항등원,identity_element을 가진다(이 특징을 semigroup과 대조해 보라.) - TBW
Contrast: semigroup
}
Monoid_(category_theory)= https://en.wikipedia.org/wiki/Monoid_(category_theory)
= https://en.wikipedia.org/wiki/Monoid_(category_theory)
