The hardest linear conjunctive language

This paper demonstrates that the P-complete language of yes-instances of Circuit Value Problem under a suitable encoding can be generated by a linear conjunctive grammar, or, equivalently, accepted by a triangular trellis automaton. This result has several implications on the properties of the languages generated by conjunctive grammars of the general form and on the relationship between the abstract models of parallel computation.     

On the descriptional complexity of scattered context grammars

This paper proves that every recursively enumerable language is generated by a scattered context grammar with no more than four nonterminals and three non-context-free productions. In its conclusion, it gives an overview of the results and open problems concerning scattered context grammars and languages.     

Nonterminal complexity of tree controlled grammars

This paper studies the nonterminal complexity of tree controlled grammars. It is proved that the number of nonterminals in tree controlled grammars without erasing rules leads to an infinite hierarchy of families of tree controlled languages, while every recursively enumerable language can be generated by a tree controlled grammar with erasing rules and at most nine nonterminals.     

Scattered context grammars generate any recursively enumerable language with two nonterminals

By showing that two nonterminals are sufficient, we present the optimal lower bound on the number of nonterminals of scattered context grammars being able to generate any recursively enumerable language.     

A characterization of s-languages

We show that a language L is an s-language if and only if the set of the quotients of L (i.e., the set of the states of its minimal deterministic automaton seen as languages) is a subset of a free monoid generated by a finite set of prefix codes. We demonstrate through examples how to use this result for deciding whether a given language is an s-language.     

On the subword complexity of locally catenative dol languages

The subword complexity of language K, denoted Gv;_K, is the function of positive integers such that Gv;_K(n) equals the number of subwords of length n that occur in (words of) K. It is proved that if K is a locally catenative DOL language, then Gv;_K is bounded by a linear function.     

On the synchronized derivation depth of context-free grammars

We consider depth of derivations as a complexity measure for synchronized and ordinary context-free grammars. This measure differs from the earlier considered synchronization depth in that it counts the depth of the entire derivation tree. We consider (non-)existence of trade-offs when using synchronized grammars as opposed to non-synchronized grammars and establish lower bounds for certain classes of linear context-free languages.     

Inequality of finite behaviors of rational weight finite automata is in R

Inequivalence of finite automata accepting finite languages over a non-unary alphabet is NP-complete. However, the inequality of their behaviors does not appear to have been carefully investigated. In the simplest case, the behavior of a finite automaton is the formal series f such that the coefficient f(w) of a word w is the number of distinct accepting computations on w. This notion will be generalized in the paper to finite automata with rational weights. The main result is that inequality of rational weight finite automata with finite behaviors is in R, random polynomial time.     

On the degree of scattered context-sensitivity

In this paper, we prove that every recursively enumerable language can be generated by a scattered context grammar with no more than two context-sensitive productions.     

On the efficient construction of quasi-reversible automata for reversible languages

Quasi-reversible automata is a suitable representation for reversible languages. In this work a method is proposed to obtain such an automaton for any given reversible language represented by its minimal DFA. Our method runs in polynomial time respect to the size of the minimal DFA and improves a previous exponential method. Previous bound for the size of quasi-reversible automata is also reduced.     

On the non-efficient PAC learnability of conjunctive queries

This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating fact that this concept class lacks the polynomial-size fitting property, a property that is tacitly assumed in much of the computational learning theory literature; (ii) we establish a strong negative PAC learnability result that applies to many restricted classes of conjunctive queries (CQs), including acyclic CQs for a wide range of notions of acyclicity; (iii) we show that CQs (and UCQs) are efficiently PAC learnable with membership queries.     

Descendants of a recognizable tree language for sets of linear monadic term rewrite rules

For a tree language L and a set S of term rewrite rules over Σ, the descendant of L for S is the set S^∗(L) of trees reachable from a tree in L by rewriting in S. For a recognizable tree language L, we study the set D(L) of descendants of L for all sets of linear monadic term rewrite rules over Σ. We show that D(L) is finite. For each tree automaton A over Σ, we can effectively construct a set {R₁,…,Rk} of linear monadic term rewrite systems over Σ such that and for any 1?i<j?k, .