The position of table languages within the hierarchy of nondeterministic on-line tape-bounded turing machine languages

Table languages are extensions of finite state languages and context free languages. Table languages have access to a table on each generation step. Table entries are an ordered pair: (attribute,identifier). The collection of attributes comprise a finite set while the collection of identifiers comprise an infinite regular set. An arbitrary table language generator is in "normal form" when it has both finite state mappings of table-identifiers to terminalidentifiers and partitioned sets of undeclared identifiers. An "alternate form" of arbitrary table language generators retains the finite state table to terminal mappings but requires that the undeclared identifiers be a unified set. This "alternate form" is shown to be equivalent to the "normal form." A partitioned table language generator is a restriction on an arbitrary table language generator having only 1:1 table to terminal mappings while retaining the partitioning of the set of undeclared identifiers. This restriction is shown to be positive. A unified table language generator is a restricted form of a partitioned table language generator having a unified set of undeclared identifiers. This restriction is shown to be positive. Twenty four distinct families of table languages are defined by two additional independent types of restrictions. The families are shown to comprise a lattice of proper containment lying between the non-deterministic on-line n3 tape-bounded Turing machine generators and the regular sets. Seven of the families are identified with the syntax of well known programming languages.