Emptiness of Zero Automata Is Decidable

Zero automata are a probabilistic extension of parity automata on infinite trees. The satisfiability of a certain probabilistic variant of MSO, called TMSO+zero, reduces to the emptiness problem for zero automata. We introduce a variant of zero automata called nonzero automata. We prove that for every zero automaton there is an equivalent nonzero automaton of quadratic size and the emptiness problem of nonzero automata is decidable, with complexity co-NP. These results imply that TMSO+zero has decidable satisfiability

Mixing Probabilistic and non-Probabilistic Objectives in Markov Decision Processes

In this paper, we consider algorithms to decide the existence of strategies in MDPs for Boolean combinations of objectives. These objectives are omega-regular properties that need to be enforced either surely, almost surely, existentially, or with non-zero probability. In this setting, relevant strategies are randomized infinite memory strategies: both infinite memory and randomization may be needed to play optimally. We provide algorithms to solve the general case of Boolean combinations and we also investigate relevant subcases. We further report on complexity bounds for these problems.Comment: Paper accepted to LICS 2020 - Full versio

Alternating Nonzero Automata

We introduce a new class of automata on infinite trees called alternating nonzero automata, which extends the class of non-deterministic nonzero automata. The emptiness problem for this class is still open, however we identify a subclass, namely limited choice, for which we reduce the emptiness problem for alternating nonzero automata to the same problem for non-deterministic ones, which implies decidability. We obtain, as corollaries, algorithms for the satisfiability of a probabilistic temporal logic extending both CTL* and the qualitative fragment of pCTL*

RUN, Xtatic, RUN: EFFICIENT IMPLEMENTATION OF AN OBJECT-ORIENTED LANGUAGE WITH REGULAR PATTERN MATCHING

Schema languages such as DTD, XML Schema, and Relax NG have been steadily growing in importance in the XML community. A schema language provides a mechanism for defining the type of XML documents; i.e., the set of constraints that specify the structure of XML documents that are acceptable as data for a certain programming task. A number of recent language designs—many of them descended from the XDuce language of Hosoya, Pierce, and Vouillon—have showed how such schemas can be used statically for type-checking XML processing code and dynamically for evaluation of XML structures. The technical foundation of such languages is the notion of regular types, a mild generalization of nondeterministic top-down tree automata, which correspond to a core of most popular schema notations, and the no-tion of regular patterns—regular types decorated with variable binders—a powerful and convenient primitive for dynamic inspection of XML values. This dissertation is concerned with one of XDuce’s descendants, Xtatic. The goal of the Xtatic project is to bring the regular type and regular pattern technologies to a wide audience by integrating them with a mainstream object-oriented language. My research focuses on an efficient implementation of Xtatic including a compiler that generates fast and compact target program

On the Regular Emptiness Problem of Subzero Automata

Subzero automata is a class of tree automata whose acceptance condition can express probabilistic constraints. Our main result is that the problem of determining if a subzero automaton accepts some regular tree is decidable

The Music Sound

A guide for music: compositions, events, forms, genres, groups, history, industry, instruments, language, live music, musicians, songs, musicology, techniques, terminology , theory, music video. Music is a human activity which involves structured and audible sounds, which is used for artistic or aesthetic, entertainment, or ceremonial purposes. The traditional or classical European aspects of music often listed are those elements given primacy in European-influenced classical music: melody, harmony, rhythm, tone color/timbre, and form. A more comprehensive list is given by stating the aspects of sound: pitch, timbre, loudness, and duration. Common terms used to discuss particular pieces include melody, which is a succession of notes heard as some sort of unit; chord, which is a simultaneity of notes heard as some sort of unit; chord progression, which is a succession of chords (simultaneity succession); harmony, which is the relationship between two or more pitches; counterpoint, which is the simultaneity and organization of different melodies; and rhythm, which is the organization of the durational aspects of music