Add implementation of Kleene's algorithm to show each regular language has a regex matching it

[yisiox]

This PR adds a proof that every regular language has some regular expression matching it.

This was achieved by the following constructions and proofs of their correctness

• Define toSingleεNFA to transform any epsilon-NFA to an equivalent one with only a single start and accept state (and the type is ExtendedState)
• Define a bijection between ExtendedState and Fin (FinEnum.card (ExtendedState σ)) to index the states
• Define pathRegex which implements Kleene's algorithm
• Define toRegex which takes an epsilon-NFA, applies toSingleεNFA on it, and computes the corresponding regex using pathRegex

The proofs of correctness chain together to yield (toRegex M).matches' = M.accepts which asserts the direction of Kleene's theorem required.

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[github-actions]

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[github-actions]

PR summary dffa0f2129

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Computability.EpsilonNFA	706	716	+10 (+1.42%)

Import changes for all files

Files	Import difference
Mathlib.Computability.EpsilonNFA	10

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Declarations diff

+ ExtendedState
+ ExtendedState.equivSum
+ IsPath.from_accept
+ IsPath.state_accept
+ IsPath.toSingleεNFA_lift_extendedState
+ IsRestrictedMatch
+ IsRestrictedMatch.mono
+ IsRestrictedPath
+ accepts_toRegex
+ accepts_toSingleεNFA
+ directRegex
+ e
+ instance [FinEnum σ] : FinEnum (ExtendedState σ)
+ instance {M : εNFA α σ}
+ isRestrictedMatch_iff_exists_isPath
+ isRestrictedMatch_iff_exists_isRestrictedPath
+ isRestrictedMatch_nil
+ isRestrictedMatch_of_mem_pathRegex
+ isRestrictedMatch_star
+ isRestrictedPath_iff_isPath
+ matches'_foldl_acc
+ matches'_foldl_sum
+ mem_matches'_directRegex
+ mem_matches_mul_star_mul
+ mem_matches_star_concat
+ mem_matches_star_singleton
+ mem_pathRegex_iff_isRestrictedMatch
+ mem_pathRegex_of_isRestrictedMatch
+ pathRegex
+ pathRegex_mono
+ pathRegex_trans
+ toRegex
+ toSingleεNFA

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for scripts/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).