Quantitative Automata under Probabilistic Semantics

Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties. For a well-studied and wide class of quantitative functions, we establish that automata with monitor counters and nested weighted automata are equivalent. We study for the first time such quantitative automata under probabilistic semantics. We show that several problems that are undecidable for the classical questions of emptiness and universality become decidable under the probabilistic semantics. We present a complete picture of decidability for such automata, and even an almost-complete picture of computational complexity, for the probabilistic questions we consider

Sublinearly space bounded iterative arrays

Iterative arrays (IAs) are a, parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this note, realtime-lAs with sublinear space bounds are used to accept formal languages. The existence of a proper hierarchy of space complexity classes between logarithmic anel linear space bounds is proved. Furthermore, an optimal spacc lower bound for non-regular language recognition is shown. Key words: Iterative arrays, cellular automata, space bounded computations, decidability questions, formal languages, theory of computatio

Disjunctive bases: normal forms and model theory for modal logics

We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central role in the proof of a generic completeness theorem for coalgebraic mu-calculi. Believing the concept has a much wider significance, here we investigate it more thoroughly in its own right. We show that the presence of a disjunctive basis at the "one-step" level entails a number of good properties for a coalgebraic mu-calculus, in particular, a simulation theorem showing that every alternating automaton can be transformed into an equivalent nondeterministic one. Based on this, we prove a Lyndon theorem for the full fixpoint logic, its fixpoint-free fragment and its one-step fragment, a Uniform Interpolation result, for both the full mu-calculus and its fixpoint-free fragment, and a Janin-Walukiewicz-style characterization theorem for the mu-calculus under slightly stronger assumptions. We also raise the questions, when a disjunctive basis exists, and how disjunctive bases are related to Moss' coalgebraic "nabla" modalities. Nabla formulas provide disjunctive bases for many coalgebraic modal logics, but there are cases where disjunctive bases give useful normal forms even when nabla formulas fail to do so, our prime example being graded modal logic. We also show that disjunctive bases are preserved by forming sums, products and compositions of coalgebraic modal logics, providing tools for modular construction of modal logics admitting disjunctive bases. Finally, we consider the problem of giving a category-theoretic formulation of disjunctive bases, and provide a partial solution

Learning About Meetings

Most people participate in meetings almost every day, multiple times a day. The study of meetings is important, but also challenging, as it requires an understanding of social signals and complex interpersonal dynamics. Our aim this work is to use a data-driven approach to the science of meetings. We provide tentative evidence that: i) it is possible to automatically detect when during the meeting a key decision is taking place, from analyzing only the local dialogue acts, ii) there are common patterns in the way social dialogue acts are interspersed throughout a meeting, iii) at the time key decisions are made, the amount of time left in the meeting can be predicted from the amount of time that has passed, iv) it is often possible to predict whether a proposal during a meeting will be accepted or rejected based entirely on the language (the set of persuasive words) used by the speaker

Formal Verification of Probabilistic SystemC Models with Statistical Model Checking

Transaction-level modeling with SystemC has been very successful in describing the behavior of embedded systems by providing high-level executable models, in which many of them have inherent probabilistic behaviors, e.g., random data and unreliable components. It thus is crucial to have both quantitative and qualitative analysis of the probabilities of system properties. Such analysis can be conducted by constructing a formal model of the system under verification and using Probabilistic Model Checking (PMC). However, this method is infeasible for large systems, due to the state space explosion. In this article, we demonstrate the successful use of Statistical Model Checking (SMC) to carry out such analysis directly from large SystemC models and allow designers to express a wide range of useful properties. The first contribution of this work is a framework to verify properties expressed in Bounded Linear Temporal Logic (BLTL) for SystemC models with both timed and probabilistic characteristics. Second, the framework allows users to expose a rich set of user-code primitives as atomic propositions in BLTL. Moreover, users can define their own fine-grained time resolution rather than the boundary of clock cycles in the SystemC simulation. The third contribution is an implementation of a statistical model checker. It contains an automatic monitor generation for producing execution traces of the model-under-verification (MUV), the mechanism for automatically instrumenting the MUV, and the interaction with statistical model checking algorithms.Comment: Journal of Software: Evolution and Process. Wiley, 2017. arXiv admin note: substantial text overlap with arXiv:1507.0818

Complexity, parallel computation and statistical physics

The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to simulate it. Depth provides an objective, irreducible measure of history applicable to systems of the kind studied in statistical physics. It is argued that physical complexity cannot occur in the absence of substantial depth and that depth is a useful proxy for physical complexity. The ideas are illustrated for a variety of systems in statistical physics.Comment: 21 pages, 7 figure

Computação quântica : autômatos, jogos e complexidade

Orientador: Arnaldo Vieira MouraDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Desde seu surgimento, Teoria da Computação tem lidado com modelos computacionais de maneira matemática e abstrata. A noção de computação eficiente foi investigada usando esses modelos sem procurar entender as capacidades e limitações inerentes ao mundo físico. A Computação Quântica representa uma ruptura com esse paradigma. Enraizada nos postulados da Mecânica Quântica, ela é capaz de atribuir um sentido físico preciso à computação segundo nosso melhor entendimento da natureza. Esses postulados dão origem a propriedades fundamentalmente diferentes, uma em especial, chamada emaranhamento, é de importância central para computação e processamento de informação. O emaranhamento captura uma noção de correlação que é única a modelos quânticos. Essas correlações quânticas podem ser mais fortes do que qualquer correlação clássica estando dessa forma no coração de algumas capacidades quânticas que vão além do clássico. Nessa dissertação, nós investigamos o emaranhamento da perspectiva da complexidade computacional quântica. Mais precisamente, nós estudamos uma classe bem conhecida, definida em termos de verificação de provas, em que um verificador tem acesso à múltiplas provas não emaranhadas (QMA(k)). Assumir que as provas não contêm correlações quânticas parece ser uma hipótese não trivial, potencialmente fazendo com que essa classe seja maior do que aquela em que há apenas uma prova. Contudo, encontrar cotas de complexidade justas para QMA(k) permanece uma questão central sem resposta por mais de uma década. Nesse contexto, nossa contribuição é tripla. Primeiramente, estudamos classes relacionadas mostrando como alguns recursos computacionais podem afetar seu poder de forma a melhorar a compreensão a respeito da própria classe QMA(k). Em seguida, estabelecemos uma relação entre Probabilistically Checkable Proofs (PCP) clássicos e QMA(k). Isso nos permite recuperar resultados conhecidos de maneira unificada e simplificada. Para finalizar essa parte, mostramos que alguns caminhos para responder essa questão em aberto estão obstruídos por dificuldades computacionais. Em um segundo momento, voltamos nossa atenção para modelos restritos de computação quântica, mais especificamente, autômatos quânticos finitos. Um modelo conhecido como Two-way Quantum Classical Finite Automaton (2QCFA) é o objeto principal de nossa pesquisa. Seu estudo tem o intuito de revelar o poder computacional provido por memória quântica de dimensão finita. Nos estendemos esse autômato com a capacidade de colocar um número finito de marcadores na fita de entrada. Para qualquer número de marcadores, mostramos que essa extensão é mais poderosa do que seus análogos clássicos determinístico e probabilístico. Além de trazer avanços em duas linhas complementares de pesquisa, essa dissertação provê uma vasta exposição a ambos os campos: complexidade computacional e autômatosAbstract: Since its inception, Theoretical Computer Science has dealt with models of computation primarily in a very abstract and mathematical way. The notion of efficient computation was investigated using these models mainly without seeking to understand the inherent capabilities and limitations of the actual physical world. In this regard, Quantum Computing represents a rupture with respect to this paradigm. Rooted on the postulates of Quantum Mechanics, it is able to attribute a precise physical notion to computation as far as our understanding of nature goes. These postulates give rise to fundamentally different properties one of which, namely entanglement, is of central importance to computation and information processing tasks. Entanglement captures a notion of correlation unique to quantum models. This quantum correlation can be stronger than any classical one, thus being at the heart of some quantum super-classical capabilities. In this thesis, we investigate entanglement from the perspective of quantum computational complexity. More precisely, we study a well known complexity class, defined in terms of proof verification, in which a verifier has access to multiple unentangled quantum proofs (QMA(k)). Assuming the proofs do not exhibit quantum correlations seems to be a non-trivial hypothesis, potentially making this class larger than the one in which only a single proof is given. Notwithstanding, finding tight complexity bounds for QMA(k) has been a central open question in quantum complexity for over a decade. In this context, our contributions are threefold. Firstly, we study closely related classes showing how computational resources may affect its power in order to shed some light on \QMA(k) itself. Secondly, we establish a relationship between classical Probabilistically Checkable Proofs and QMA(k) allowing us to recover known results in unified and simplified way, besides exposing the interplay between them. Thirdly, we show that some paths to settle this open question are obstructed by computational hardness. In a second moment, we turn our attention to restricted models of quantum computation, more specifically, quantum finite automata. A model known as Two-way Quantum Classical Finite Automaton (2QCFA) is the main object of our inquiry. Its study is intended to reveal the computational power provided by finite dimensional quantum memory. We extend this automaton with the capability of placing a finite number of markers in the input tape. For any number of markers, we show that this extension is more powerful than its classical deterministic and probabilistic analogues. Besides bringing advances to these two complementary lines of inquiry, this thesis also provides a vast exposition to both subjects: computational complexity and automata theoryMestradoCiência da ComputaçãoMestre em Ciência da Computaçã