Alexander Ja. Dikovsky

Categorial dependency grammars

Categorial Dependency Grammars (CDGs) are classical categorial grammars extended by oriented polarized valencies. At the same time, CDGs represent a class of completely lexicalized dependency grammars. They express both projective and non-projective dependencies. CDGs generate non-context-free languages. At that, they are parsed in polynomial time under realistic conditions. CDGs possess a normal form that is analogous to Greibach normal form for cf-grammars. CDG-languages are closed under almost all AFL operations and are accepted by a special class of push-down automata with independent counters.

Generalized categorial dependency grammars

Generalized Categorial Dependency Grammars (gCDG) studied in this paper are genuine categorial grammars expressing projective and discontinuous dependencies, stronger than CF-grammars and non-equivalent to mild context-sensitive grammars. We show that gCDG are parsed in polynomial time and enjoy good mathematical properties.

Temporal verification of probabilistic multi-agent systems

Probabilistic systems of interacting intelligent agents are considered. They have two sources of uncertainty: uncertainty of communication channels and uncertainty of actions. We show how such systems can be polynomially transformed to finite state Markov chains. This allows one to transfer known results on verifying temporal properties of the finite state Markov chains to the probabilistic multi-agent systems of the considered type.

Dependency structure grammars

In this paper, we define Dependency Structure Grammars (DSG), which are rewriting rule grammars generating sentences together with their dependency structures, are more expressive than CF-grammars and non-equivalent to mildly context-sensitive grammars. We show that DSG are weakly equivalent to Categorial Dependency Grammars (CDG) recently introduced in [6,3]. In particular, these dependency grammars naturally express long distance dependencies and enjoy good mathematical properties.

Complexity of Multi-agent Systems Behavior

The complexity of multi-agent systems behavior properties is studied. The behavior properties are formulated using first order temporal logic languages and are checked relative to the state transition diagram induced by the multi-agent system. Various tight complexity bounds of the behavior properties are established under natural structural and semantic restrictions on agent programs and actions. There are some interesting cases, where the check problem is decidable in deterministic or nondeterministic polynomial time.

Polarized Non-projective Dependency Grammars

Dependency tree grammars are proposed in which unbounded discontinuity is resolved through the first available valency saturation. In general, they are expressive enough to generate non-semilinear context sensitive languages, but in the practical situation where the number of non saturated valencies is bounded by a constant, they are weakly equivalent to cf-grammars, are parsable in cubic time, and are stronger than non-projective dependency grammars without long dependencies.

Grammars for Local and Long Dependencies

Polarized dependency (PD-) grammars are proposed as a means of efficient treatment of discontinuous constructions. PD-grammars describe two kinds of dependencies: local, explicitly derived by the rules, and long, implicitly specified by negative and positive valencies of words. If in a PD-grammar the number of non-saturated valencies in derived structures is bounded by a constant, then it is weakly equivalent to a cf-grammar and has a O(n3)-time parsing algorithm. It happens that such bounded PD-grammars are strong enough to express such phenomena as unbounded raising, extraction and extraposition.

On Homeostatic Behavior of Dynamic Deductive Data Bases

We define a new property of steady behavior of dynamic deductive data bases interacting with their active medium. This property is in fact the homeostaticity, i.e. the ability of the database to restore its integrity constraints after ruinous disturbances of its medium. The formal model we use is based on a new concept, that of bounded disturbance of an active medium. We explore the computational complexity of this property in various classes of dynamic deductive data bases.

Two models of learning iterated dependencies

We study the learnability problem in the family of Categorial Dependency Grammars (CDG), a class of categorial grammars defining unlimited dependency structures. CDG satisfying a reasonable condition on iterated (i.e., repeatable and optional) dependencies are shown to be incrementally learnable in the limit.

Iterated dependencies and Kleene iteration

Categorial Dependency Grammars (CDG) is a class of simple and expressive categorial grammars defining projective and discontinuous dependency structures in a strongly compositional way. They are more expressive than CF-grammars, are polynomial time recognizable and different from the mildly context sensitive grammars. CDG languages are proved to be closed under all AFL operations, but iteration. In this paper, we explain the connection between the iteration closure and the iterated dependencies (optional repeatable dependencies, inevitable in dependency syntax) and show that the CDG extended by a natural multimodal rule define an AFL, but the membership problem in this extended family is NP-complete.