Macro Grammars Research Articles

On the Generative Power of Multiple Context-Free Grammars and Macro Grammars

Several grammars of which generative power is between context-free grammar and context-sensitive grammar were proposed. Among them are macro grammar and tree adjoining grammar. Multiple context-free grammar is also a natural extension of context-free grammars, and is known to be stronger in its generative power than tree adjoining grammar and yet to be recognizable in polynomial time. In this paper, the generative power of several subclasses of variable-linear macro grammars and that of multiple context-free grammars are compared in details.

An automata-theoretical characterization of the OI-hierarchy

This paper gives an automata-theoretical characterization of the OI-hierarchy (Damm (1982), Engelfriet and Schmidt (1977), Wand (1975)). This hierarchy is generated by so-called level-n grammars which are natural generalizations from context free and macro grammars in that their nonterminals are treated as functionals of higher type, i.e., they are allowed to carry up to n levels of parameters. The automata model used for this characterization is the n-iterated pushdown automaton. Its characteristic feature is the storage structure which consists of a nesting of pushdowns up to nesting depth n. The equivalence proof is given constructively, its method is illustrated using examples. By viewing level-n grammars as modeling recursive procedures on higher types the iterated pushdown automation thus provides an operational model for the run-time behavior of procedures defined by recursion on higher types which makes the results of this paper interesting not only from a language theoretical point of view.

Macro tree transducers

Macro tree transducers are a combination of top-down tree transducers and macro grammars. They serve as a model for syntax-directed semantics in which context information can be handled. In this paper the formal model of macro tree transducers is studied by investigating typical automata theoretical topics like composition, decomposition, domains, and ranges of the induced translation classes. The extension with regular look-ahead is considered.

Hierarchies of hyper-AFLs

For a full semi-AFL K, B( K) is defined as the family of languages generated by all K-extended basic macro grammars, while H( K) ⊆ B( K) is the smallest full hyper-AFL containing K; a full basic-AFL is a full AFL K such that B( K) = K (hence every full basic-AFL is a full hyper-AFL). For any full semi-AFL K, K is a full basic-AFL if and only if B( K) is substitution closed if and only if H( K) is a full basic-AFL. If K is not a full basic-AFL, then the smallest full basic-AFL containing K is the union of an infinite hierarchy of full hyper-AFLs. If K is a full principal basic-AFL (such as INDEX, the family of indexed languages), then the largest full AFL properly contained in K is a full basic-AFL. There is a full basic-AFL lying properly in between the smallest full basic-AFL and the largest full basic-AFL in INDEX.

Extended macro grammars and stack controlled machines

K-extended basic macro grammars are introduced, where K is any class of languages. The class B(K) of languages generated by such grammars is investigated, together with the class LB(K) of languages generated by the corresponding linear basic grammars. For any full semi-AFL K, B(K) is a full AFL closed under iterated LB(K)-substitution, but not necessarily under substitution. For any machine type D, the stack controlled machine type corresponding to D is introduced, denoted S(D), and the checking-stack controlled machine type CS(D). The data structure of this machine is a stack which controls a pushdown of data structures from D. If D accepts K, then S(D) accepts B(K) and CS(D) accepts LB(K). Thus the classes B(K) are characterized by stack controlled machines and the classes LB(K), i.e., the full hyper-AFLs, by checking-stack controlled machines. A full basic-AFL is a full AFL K such that B( K) ⊆ K. Every full basic-AFL is a full hyper-AFL, but not vice versa. The class of OI macro languages (i.e., indexed languages, i.e., nested stack automaton languages) is a full basic-AFL, properly containing the smallest full basic-AFL. The latter is generated by the ultrabasic macro grammars and accepted by the nested stack automata with bounded depth of nesting (and properly contains the stack languages, the ETOL languages, i.e., the smallest full hyper-AFL, and the basic macro languages). The full basic-AFLs are characterized by bounded nested stack controlled machines.

Bounded nesting in macro grammars

Macro grammars and context-free tree grammars are discussed in which a bound is put (dynamically or statically) on the nesting-depth of nested calls of nonterminals. The dynamic and static restrictions are closely related (and both are related to the nested stack automaton with bounded nesting of stacks). The corresponding classes of tree languages have derivation bounded contextfree languages as path-languages. Macro languages exist which cannot be generated by nesting-depth bounded macro grammars.

Parsing macro grammars top down

A top-down parsing scheme for macro grammars is proposed. It extends the recursive descent method frequently used in context-free parsing. It is shown to be decidable if a macro grammar is top-down parsable. Nearly matching lower and upper bounds for the complexity of the decision procedure are derived. A time and space efficient recognition algorithm is described.

Extended linear macro grammars, iteration grammars, and register programs

Extended macro grammars (of the linear basic type only) are introduced as a generalization of those in [5], and it is shown that they have the same language generating power as (parallel) iteration grammars. In particular the IO and OI versions of extended macro grammars correspond to the deterministic and the (usual) nondeterministic iteration grammars respectively. Hence iterated substitution can be formulated using extended macro grammars. A nondeterministic register program without tests may be viewed as a macro grammar. IO-extension of this macro grammar corresponds to the use of nonrecursive function procedures in the register program. OI-extended macro grammars correspond to register programs which compute on sets. Hence these features of register programs can be investigated by means of (extended) parallel rewriting systems.

Succinctness of Descriptions of Context-Free, Regular, and Finite Languages

<p>This thesis analyzes the descriptional power of finite automata, regular expressions, pushdown automata, and certain generalized models of macro grammars. For finite automata and pushdown automata the emphasis is on ambiguity. It is shown that ambiguous nondeterminism allows more succinct definitions than unambiguous nondeterminism which in turn allows more succinct definitions than determinism. The succinctness gain is nonrecursive for pda's and nonpolynomial for finite automata.</p><p>The succinctness of regular expressions and macro grammars is measured in terms of complexity theory. It is shown that the inequivalence problem for Ol macro grammars generating finite languages is hard for nondeterministic double exponential time, and that the ''nonemptiness of complement'' problem for unambiguous regular expressions is in NP. This implies that unambiguous regular expressions are ''easier'' than general regular expressions (unless NP is equal to PSPACE).</p>

On procedures as open subroutines. II

In part I [11] of the paper elimination of global procedure parameters and modularity of programming languages have been investigated. The methods developed there are used in the present part II to prove that the so called macro program problem for ALGOL 60 and other ALGOL-like languages is algorithmically unsolvable (Theorem 4.3 and 4.4). Macro grammars theory is applied in order to determine sublanguages for which the macro program problem is solvable (Theorem 4.1, 5.2---5.5).