CYK algorithm

Let the input be a string S consisting of n characters: a1 ... an.
Let the grammar contain r nonterminal symbols R1 ... Rr.
This grammar contains the subset Rs which is the set of start symbols.
Let P[n,n,r] be an array of booleans. Initialize all elements of P to false.
For each i = 1 to n
  For each unit production Rj -> ai, set P[i,1,j] = true.
For each i = 2 to n -- Length of span
  For each j = 1 to n-i+1 -- Start of span
    For each k = 1 to i-1 -- Partition of span
      For each production RA -> RB RC
        If P[j,k,B] and P[j+k,i-k,C] then set P[j,i,A] = true
If any of P[1,n,x] is true (x is iterated over the set s, where s are all the indices for Rs)
  Then S is member of language
Else S is not member of language

As prose
In informal terms, this algorithm considers every possible subsequence of the sequence of words and sets P[i,j,k] to be true if the subsequence of words starting from i of length j can be generated from Rk. Once it has considered subsequences of length 1, it goes on to subsequences of length 2, and so on. For subsequences of length 2 and greater, it considers every possible partition of the subsequence into two parts, and checks to see if there is some production P → Q R such that Q matches the first part and R matches the second part. If so, it records P as matching the whole subsequence. Once this process is completed, the sentence is recognized by the grammar if the subsequence containing the entire sentence is matched by the start symbol.