J. Bresnan and R. M. Kaplan introduced lexical-functional grammars (LFGs, for short) as a new formalism for human language syntax. It is important to show formal properties of this kind of grammars in order to characterize the formal complexity of human languages. In this paper, we will show that the emptiness problem for LFGs is undecidable.

We are concerned with a subclass of deterministic pushdown automata (dpda) called very simple dpda's, and present a new direct branching algorithm for checking the inclusion for a pair of languages accepted by these dpda's. As usual, we take the maximal thickness (i.e., the length of the shortest input strings that make each stack symbol go to empry) of all stack symbols into account as one parameter of the given dpda's. Then the worst-case time complexity of our algorithm is polynomial with respect to these parameters. Without considering the thickness, the complexity is single exponential in the description length of the given dpda's. As far as we are concerned with very simple dpda's, our algorithm is very simple and direct, and is faster and much better than the previously given algorithms for the inclusion problem of dpda's.

When a group of developers are involved in the distributed development of some software product, they must communicate with one another frequently to exchange information about the product. To reduce the penalty of communication, the support environment should provide developers with their necessary information and update the information automatically while the product is modified by developers. Furthermore, the environment must meet the following requirements despite of workstation failures: whether a specific information is correct or not should always be decidable; as much information as possible should be updated correctly and efficiently. This paper presents a framework to construct such a fault-tolerant environment based on attribute grammars. In the framework, a product is represented by an attributed tree, which is partitioned into several subtrees {T1,,Tm}. Attribute values in each subtree Ti(1im) express the information about the product required by a developer. We introduce a set of redundant data and algorithms to meet the fault-tolerance requirements mentioned above. The correctness of an attribute value in Ti can then be decided in O(mn0log n) time, where n0n, and n is the number of attribute instances in Ti. All available attribute values can be updated with time complexity O(m2n1 log n) and communication complexity O(m2), where n1 is the number of attribute instances that must be reevaluated.

CFGs (context-free grammars) with various types of memory are introduced and their generative capacities are investigated. For an automata-theoretic characterization, a new type of automaton called partitioning automaton is introduced and it is shown that the class of languages generated by CFGs with memory type X is equal to the class of languages accepted by partitioning automata of type X.

Parallel multiple context-free grammars (pmcfg's) and multiple context-free grammars (mcfg's) were introduced as extensions of context-free grammars to describe the syntax of natural languages. Pmcfg's and mcfg's deal with tuples of strings, and it has been shown that the universal recognition problem for mcfg's is EXP-POLY time-complete where the universal recognition problem is the problem to decide whether G generates w for a given grammar G and string w. In this paper, the universal recognition problems for the class of pmcfg's and for the subclass of pmcfg's with the information-lossless condition are shown to be EXP-POLY time-complete and PSPACE-complete, respectively. It is also shown that the problems for pmcfg's and for mcfg's with a bounded dimension are both -complete and those for pmcfg's and for mcfg's with a bounded degree are both -complete. As a corollary, the problem for modified head grammars introduced by Vijay-Shanker, et al. to define the syntax of natural languages is shown to be in deterministic polynomial time.

Syntax-directed editors have several advantages in editing programs because programming is guided by the syntax and free from syntax errors. Nevertheless, they are less popular than text editiors. One of the reason is that they force a priori specified editing structures on the user and do not allow him to use his own structure. ACE (Algorithmically Customizable syntax-directed Editor) provides a solution for this problem by using a technique of machine learning; ACE has a special function of customizing the grammar algorithmically and interactively based on the learning method for grammars from examples and queries. The grammar used in the editor is customized through interaction with the user so that the user can edit his program in a more familiar structure. The customizing function has been implemented based on the methods for learning of context-free grammars from structural examples, for which the correctness and the efficiency are proved formally. This guarantees the soundness and the efficiency of customization. Furthermore, ACE can be used as an algorithmic and interactive tool to design grammars, which is required for several purposes such as compiler design and pretty-printer design.

Lexical-Functional Grammars (LFG's) were introduced to define the syntax of natural languages. In LFG's, each node of a derivation tree has some attributes. An LFG G consists of a context-free grammar (cfg) G0 called the underlying cfg of G and a description Pfs of constraints between the values of the attributes. Pfs can specify (1) constraints between the value of an attribute of a node and those of its children, and (2) constraints between the value of an attribute of a node called a controller and that of a node called its controllee. RLFG's were introduced as a subclass of LFG's. In RLFG's, only constraints between the value of an attribute of a node and those of its children can be specified. It is shown in this paper that the class of languages generated by RLFG's is equal to the class of recursively enumerable languages. Some restrictions on LFG's were proposed for the purpose of efficient parsing. Among them are (1) the condition called a valid derivation, and (2) the condition that the underlying cfg is cycle-free. For an RLFG G, if the production rules of the underlying cfg of G are of the form AaB or Aa for nonterminal symbols A, B and a terminal symbol a, then G is called an R-RLFG. Every R-RLFG satisfies the above restriction (1) and (2). It is also shown in this paper that the class of languages generated by R-RLFG's contains an NP-hard language, which means that parsing in deterministic polynomial time of LFG's is impossible in general (unless PNP) even if the above restrictions (1) and (2) are satisfied.

Multiple context-free grammars (mcfg's) are a subclass of generalized context-free grammars introduced by Pollard in order to describe the syntax of natural languages. First, this paper shows that the universal recognition problem for mcfg's is EXP-POLY time-complete, where the universal recognition problem is the one to decide whether G generates w for a given grammar G and string w. Next, it is shown that the problem for linear context-free rewriting systems introduced by Vijay-Shanker et al., which is a proper subclass of mcfg's, is PSPACE-complete.