Different Approaches to Proof Systems

The classical approach to proof complexity perceives proof systems as deterministic, uniform, surjective, polynomial-time computable functions that map strings to (propositional) tautologies. This approach has been intensively studied since the late 70’s and a lot of progress has been made. During the last years research was started investigating alternative notions of proof systems. There are interesting results stemming from dropping the uniformity requirement, allowing oracle access, using quantum computations, or employing probabilism. These lead to different notions of proof systems for which we survey recent results in this paper

Deterministic Automata for Unordered Trees

Automata for unordered unranked trees are relevant for defining schemas and queries for data trees in Json or Xml format. While the existing notions are well-investigated concerning expressiveness, they all lack a proper notion of determinism, which makes it difficult to distinguish subclasses of automata for which problems such as inclusion, equivalence, and minimization can be solved efficiently. In this paper, we propose and investigate different notions of "horizontal determinism", starting from automata for unranked trees in which the horizontal evaluation is performed by finite state automata. We show that a restriction to confluent horizontal evaluation leads to polynomial-time emptiness and universality, but still suffers from coNP-completeness of the emptiness of binary intersections. Finally, efficient algorithms can be obtained by imposing an order of horizontal evaluation globally for all automata in the class. Depending on the choice of the order, we obtain different classes of automata, each of which has the same expressiveness as CMso.Comment: In Proceedings GandALF 2014, arXiv:1408.556

Isolation and characterization of Alicycliphilus denitrificans strain BC, which grows on benzene with chlorate as the electron acceptor

A bacterium, strain BC, was isolated from a benzene-degrading chlorate-reducing enrichment culture. Strain BC degrades benzene in conjunction with chlorate reduction. Cells of strain BC are short rods that are 0.6 microm wide and 1 to 2 microm long, are motile, and stain gram negative. Strain BC grows on benzene and some other aromatic compounds with oxygen or in the absence of oxygen with chlorate as the electron acceptor. Strain BC is a denitrifying bacterium, but it is not able to grow on benzene with nitrate. The closest cultured relative is Alicycliphilus denitrificans type strain K601, a cyclohexanol-degrading nitrate-reducing betaproteobacterium. Chlorate reductase (0.4 U/mg protein) and chlorite dismutase (5.7 U/mg protein) activities in cell extracts of strain BC were determined. Gene sequences encoding a known chlorite dismutase (cld) were not detected in strain BC by using the PCR primers described in previous studies. As physiological and biochemical data indicated that there was oxygenation of benzene during growth with chlorate, a strategy was developed to detect genes encoding monooxygenase and dioxygenase enzymes potentially involved in benzene degradation in strain BC. Using primer sets designed to amplify members of distinct evolutionary branches in the catabolic families involved in benzene biodegradation, two oxygenase genes putatively encoding the enzymes performing the initial successive monooxygenations (BC-BMOa) and the cleavage of catechol (BC-C23O) were detected. Our findings suggest that oxygen formed by dismutation of chlorite can be used to attack organic molecules by means of oxygenases, as exemplified with benzene. Thus, aerobic pathways can be employed under conditions in which no external oxygen is supplie

Learning Moore Machines from Input-Output Traces

The problem of learning automata from example traces (but no equivalence or membership queries) is fundamental in automata learning theory and practice. In this paper we study this problem for finite state machines with inputs and outputs, and in particular for Moore machines. We develop three algorithms for solving this problem: (1) the PTAP algorithm, which transforms a set of input-output traces into an incomplete Moore machine and then completes the machine with self-loops; (2) the PRPNI algorithm, which uses the well-known RPNI algorithm for automata learning to learn a product of automata encoding a Moore machine; and (3) the MooreMI algorithm, which directly learns a Moore machine using PTAP extended with state merging. We prove that MooreMI has the fundamental identification in the limit property. We also compare the algorithms experimentally in terms of the size of the learned machine and several notions of accuracy, introduced in this paper. Finally, we compare with OSTIA, an algorithm that learns a more general class of transducers, and find that OSTIA generally does not learn a Moore machine, even when fed with a characteristic sample

A Bibliography on Fuzzy Automata, Grammars and Lanuages

This bibliography contains references to papers on fuzzy formal languages, the generation of fuzzy languages by means of fuzzy grammars, the recognition of fuzzy languages by fuzzy automata and machines, as well as some applications of fuzzy set theory to syntactic pattern recognition, linguistics and natural language processing

On the Complexity of the Word Problem for Automaton Semigroups and Automaton Groups

In this paper, we study the word problem for automaton semigroups and automaton groups from a complexity point of view. As an intermediate concept between automaton semigroups and automaton groups, we introduce automaton-inverse semigroups, which are generated by partial, yet invertible automata. We show that there is an automaton-inverse semigroup and, thus, an automaton semigroup with a PSPACE-complete word problem. We also show that there is an automaton group for which the word problem with a single rational constraint is PSPACE-complete. Additionally, we provide simpler constructions for the uniform word problems of these classes. For the uniform word problem for automaton groups (without rational constraints), we show NL-hardness. Finally, we investigate a question asked by Cain about a better upper bound for the length of a word on which two distinct elements of an automaton semigroup must act differently