From 868f4e203fa14bad3bd152bdb1df90bff8851d44 Mon Sep 17 00:00:00 2001 From: Joscha Date: Thu, 31 Oct 2019 20:16:52 +0000 Subject: [PATCH] Add conversion example --- README.md | 27 ++++++++++++++++++++++----- resources/conversion_example_dfa.png | Bin 0 -> 54319 bytes resources/conversion_example_nfa.png | Bin 0 -> 23422 bytes 3 files changed, 22 insertions(+), 5 deletions(-) create mode 100644 resources/conversion_example_dfa.png create mode 100644 resources/conversion_example_nfa.png diff --git a/README.md b/README.md index 83adf04..2e3923f 100644 --- a/README.md +++ b/README.md @@ -13,17 +13,35 @@ The representation of DFAs and NFAs assumes an infinite alphabet: *except* a specified set. In the visualisation, the character `Σ` denotes the alphabet of tokens. -## Example +## Example NFA-to-DFA conversion -This example minimizes the DFA shown on the +This example ghci session converts the NFA shown on the +[wikipedia article about the powerset construction](https://en.wikipedia.org/wiki/Powerset_construction) +into a DFA, using the aforementioned powerset construction. + +The conversion assumes that tokens other than `0` and `1` may appear +in the input. Because of this, the resulting DFA looks different from +the one on wikipedia. + +``` haskell +>>> Just a = nfa [ (1,[(only "0",2)],[3]), (2,[(only "1",2),(only "1",4)],[]), (3,[(only "0",4)],[2]), (4,[(only "0",3)],[]) ] (1::Int) [3,4] +>>> saveDotAsPng "nfa.png" $ nfaToDot a +``` +![](resources/conversion_example_nfa.png) +``` haskell +>>> saveDotAsPng "dfa.png" $ dfaToDot $ nfaToDfa a +``` +![](resources/conversion_example_dfa.png) + +## Example DFA minimization + +This example ghci session minimizes the DFA shown on the [wikipedia article about DFA minimization](https://en.wikipedia.org/wiki/DFA_minimization). Transitions for the token `1` are specified explicitly (where necessary), while transitions for the token `0` are represented by the default transition marked with `*`. -This ghci session shows the minimization of the DFA mentioned above. - ``` haskell >>> Just a = dfa [ ("a",[('1',"c")],"b"), ("b",[('1',"d")],"a"), ("c",[('1',"f")],"e"), ("d",[('1',"f")],"e"), ("e",[('1',"f")],"e"), ("f",[],"f") ] "a" ["c","d","e"] >>> saveDotAsPng "dfa.png" $ dfaToDot a @@ -33,4 +51,3 @@ This ghci session shows the minimization of the DFA mentioned above. >>> saveDotAsPng "dfa_minimized.png" $ dfaToDot $ minimizeDfa a ``` ![](resources/minimization_example_dfa_minimized.png) - diff --git a/resources/conversion_example_dfa.png b/resources/conversion_example_dfa.png new file mode 100644 index 0000000000000000000000000000000000000000..a05b65ca86a6ab95a83a48158b7f305bedc3158a GIT binary patch literal 54319 zcmeAS@N?(olHy`uVBq!ia0y~yU{qjWU@qWbVqjok_@Kbaz`($k|H*Y 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