Kernel methods for learning languages

This paper studies a novel paradigm for learning formal languages from positive and negative examples which consists of mapping strings to an appropriate high-dimensional feature space and learning a separating hyperplane in that space. Such mappings can often be represented flexibly with string kernels, with the additional benefit of computational efficiency. The paradigm inspected can thus be viewed as that of using kernel methods for learning languages.     

Quantum automata for some multiperiodic languages

We exhibit small size measure-once one-way quantum finite automata (mo-1qfa’s) inducing multiperiodic stochastic events. Moreover, for certain classes of multiperiodic languages, we exhibit: (i) isolated cut point mo-1qfa’s whose size logarithmically depends on the periods; (ii) Monte Carlo mo-1qfa’s whose size logarithmically depends on the periods and polynomially on the inverse of the error probability.     

On a class of languages recognizable by probabilistic reversible decide-and-halt automata

We analyze the properties of probabilistic reversible decide-and-halt automata (DH-PRA) and show that there is a strong relationship between DH-PRA and 1-way quantum automata. We show that a general class of regular languages is not recognizable by DH-PRA by proving that two “forbidden” constructions in minimal deterministic automata correspond to languages not recognizable by DH-PRA. The shown class is identical to a class known to be not recognizable by 1-way quantum automata. We also prove that the class of languages recognizable by DH-PRA is not closed under union and other non-trivial Boolean operations.     

A note on two-dimensional probabilistic finite automata

This note introduces two-dimensional probabilistic finite automata (2-pfa's), and investigates several properties of them. We first show that the class of sets recognized by 2-pfa's with bounded error probability, 2-PFA, is incomparable with the class of sets accepted by two-dimensional alternating finite automata. We then show that 2-PFA is not closed under row catenation, column catenation, row +, and column + operations in Siromoney et al. (G. Siromoney, R. Siromoney, K. Krithivasan, Inform. and Control 22 (1973) 447).     

Toward diagrammability and efficiency in event-sequence languages

Many industrial verification teams are developing suitable event-sequence languages for hardware verification. Such languages must be expressive, designer friendly, and hardware specific, as well as efficient to verify. While the formal verification community has formal models for assessing the efficiency of an event-sequence language, none of these models also accounts for designer friendliness. We propose an intermediate language for event sequences that addresses both concerns. The language achieves usability through a correlation to timing diagrams; its efficiency arises from its mapping into deterministic weak automata. We present the language, relate it to existing event-sequence languages, and prove its relationship to deterministic weak automata. These results indicate that timing diagrams can become more expressive while remaining more efficient for symbolic model checking than LTL.     

A model for the formal definition of programming languages

An operational model which allows the complete formal definition of the full syntax and, particularly, semantics of programming languages is described. Both its syntactic and semantic parts are based on so-called linked-forest manipulation systems which allow the definition of mappings on forests. The idea of “linking” is crucial for the given model, we represent not only abstract programs but also intermediate states of our system (abstract computer) by labelled forests with pointers.     

A framework to visualize equivalences between computational models of regular languages

We discuss how to increase and simplify the understanding of the equivalence relations between machine models and/or language representations of formal languages by means of the animation tool SAGEMoLiC. Our new educational tool permits the simulation of the execution of models of computation, as many other animation systems do, but its philosophy goes further than these of the usual systems since it allows for a true visualization of the key notions involved in the formal proofs of these equivalences. In contrast with the proposal of previous systems, our approach to visualize equivalence theorems is not a simple “step by step animation” of specific conversion algorithms between computational models and/or grammatical representations of formal languages, because we make emphasis on the key theoretical notions involved in the formal proofs of these equivalences.     

On pebble automata for data languages with decidable emptiness problem

In this paper we study a subclass of pebble automata (PA) for data languages for which the emptiness problem is decidable. Namely, we show that the emptiness problem for weak 2-pebble automata is decidable, while the same problem for weak 3-pebble automata is undecidable. We also introduce the so-called top view weak PA. Roughly speaking, top view weak PA are weak PA where the equality test is performed only between the data values seen by the two most recently placed pebbles. The emptiness problem for this model is still decidable. It is also robust: alternating, non-deterministic and deterministic top view weak PA have the same recognition power; and are strong enough to accept all data languages expressible in Linear Temporal Logic with the future-time operators, augmented with one register freeze quantifier.     

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.     

Some Notes on Graph Automata, TilingSystems and Partition Logic

Introduce heuristically the newly definition(W.Thomas)for graph automata-using “tiles”to simulate the extension(over dag‘s) of the classical notions of transition moves;propose a sufficient condition for when graph automata can be reduced to (simpler)tiling systems,which is a generalization of a Thomas‘ result;and finally study the logic sepcification of tiling systems (particularly,over picture languages)by (existential)monadic partition logic,instead of the ususal and stronger framework(E)MSO.