Generalized simulation relations with applications in automata theory

Finite-state automata are a central computational model in computer science, with numerous and diverse applications. In one such application, viz. model-checking, automata over infinite words play a central rˆole. In this thesis, we concentrate on B¨uchi automata (BA), which are arguably the simplest finite-state model recognizing languages of infinite words. Two algorithmic problems are paramount in the theory of automata: language inclusion and automata minimization. They are both PSPACE-complete, thus under standard complexity-theoretic assumptions no deterministic algorithm with worst case polynomial time can be expected. In this thesis, we develop techniques to tackle these problems. In automata minimization, one seeks the smallest automaton recognizing a given language (“small” means with few states). Despite PSPACE-hardness of minimization, the size of an automaton can often be reduced substantially by means of quotienting. In quotienting, states deemed equivalent according to a given equivalence are merged together; if this merging operation preserves the language, then the equivalence is said to be Good for Quotienting (GFQ). In general, quotienting cannot achieve exact minimization, but, in practice, it can still offer a very good reduction in size. The central topic of this thesis is the design of GFQ equivalences for B¨uchi automata. A particularly successful approach to the design of GFQ equivalences is based on simulation relations. Simulation relations are a powerful tool to compare the local behavior of automata. The main contribution of this thesis is to generalize simulations, by relaxing locality in three perpendicular ways: by fixing the input word in advance (fixed-word simulations, Ch. 3), by allowing jumps (jumping simulations, Ch. 4), and by using multiple pebbles (multipebble simulations for alternating BA, Ch. 5). In each case, we show that our generalized simulations induce GFQ equivalences. For fixed-word simulation, we argue that it is the coarsest GFQ simulation implying language inclusion, by showing that it subsumes a natural hierarchy of GFQ multipebble simulations. From a theoretical perspective, our study significantly extends the theory of simulations for BA; relaxing locality is a general principle, and it may find useful applications outside automata theory. From a practical perspective, we obtain GFQ equivalences coarser than previously possible. This yields smaller quotient automata, which is beneficial in applications. Finally, we show how simulation relations have recently been applied to significantly optimize exact (exponential) language inclusion algorithms (Ch. 6), thus extending their practical applicability

Łukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems

A novel approach to self-organizing, highly-complex systems (HCS), such as living organisms and artificial intelligent systems (AIs), is presented which is relevant to Cognition, Medical Bioinformatics and Computational Neuroscience. Quantum Automata (QAs) were defined in our previous work as generalized, probabilistic automata with quantum state spaces (Baianu, 1971). Their next-state functions operate through transitions between quantum states defined by the quantum equations of motion in the Schroedinger representation, with both initial and boundary conditions in space-time. Such quantum automata operate with a quantum logic, or Q-logic, significantly different from either Boolean or Łukasiewicz many-valued logic. A new theorem is proposed which states that the category of quantum automata and automata--homomorphisms has both limits and colimits. Therefore, both categories of quantum automata and classical automata (sequential machines) are bicomplete. A second new theorem establishes that the standard automata category is a subcategory of the quantum automata category. The quantum automata category has a faithful representation in the category of Generalized (M,R)--Systems which are open, dynamic biosystem networks with defined biological relations that represent physiological functions of primordial organisms, single cells and higher organisms

An expressive completeness theorem for coalgebraic modal mu-calculi

Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic interpreted over coalgebras for an arbitrary set functor. We then consider invariance under behavioral equivalence of MSO-formulas. More specifically, we investigate whether the coalgebraic mu-calculus is the bisimulation-invariant fragment of the monadic second-order language for a given functor. Using automatatheoretic techniques and building on recent results by the third author, we show that in order to provide such a characterization result it suffices to find what we call an adequate uniform construction for the coalgebraic type functor. As direct applications of this result we obtain a partly new proof of the Janin-Walukiewicz Theorem for the modal mu-calculus, avoiding the use of syntactic normal forms, and bisimulation invariance results for the bag functor (graded modal logic) and all exponential polynomial functors (including the "game functor"). As a more involved application, involving additional non-trivial ideas, we also derive a characterization theorem for the monotone modal mu-calculus, with respect to a natural monadic second-order language for monotone neighborhood models.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0721

Quantum Genetics, Quantum Automata and Quantum Computation

The concepts of quantum automata and quantum computation are studied in the context of quantum genetics and genetic networks with nonlinear dynamics. In a previous publication (Baianu,1971a) the formal concept of quantum automaton was introduced and its possible implications for genetic and metabolic activities in living cells and organisms were considered. This was followed by a report on quantum and abstract, symbolic computation based on the theory of categories, functors and natural transformations (Baianu,1971b). The notions of topological semigroup, quantum automaton,or quantum computer, were then suggested with a view to their potential applications to the analogous simulation of biological systems, and especially genetic activities and nonlinear dynamics in genetic networks. Further, detailed studies of nonlinear dynamics in genetic networks were carried out in categories of n-valued, Lukasiewicz Logic Algebras that showed significant dissimilarities (Baianu, 1977) from Bolean models of human neural networks (McCullough and Pitts,1945). Molecular models in terms of categories, functors and natural transformations were then formulated for uni-molecular chemical transformations, multi-molecular chemical and biochemical transformations (Baianu, 1983,2004a). Previous applications of computer modeling, classical automata theory, and relational biology to molecular biology, oncogenesis and medicine were extensively reviewed and several important conclusions were reached regarding both the potential and limitations of the computation-assisted modeling of biological systems, and especially complex organisms such as Homo sapiens sapiens(Baianu,1987). Novel approaches to solving the realization problems of Relational Biology models in Complex System Biology are introduced in terms of natural transformations between functors of such molecular categories. Several applications of such natural transformations of functors were then presented to protein biosynthesis, embryogenesis and nuclear transplant experiments. Other possible realizations in Molecular Biology and Relational Biology of Organisms are here suggested in terms of quantum automata models of Quantum Genetics and Interactomics. Future developments of this novel approach are likely to also include: Fuzzy Relations in Biology and Epigenomics, Relational Biology modeling of Complex Immunological and Hormonal regulatory systems, n-categories and Topoi of Lukasiewicz Logic Algebras and Intuitionistic Logic (Heyting) Algebras for modeling nonlinear dynamics and cognitive processes in complex neural networks that are present in the human brain, as well as stochastic modeling of genetic networks in Lukasiewicz Logic Algebras

Deceleration in The Micro Traffic Model and Its Application to Simulation for Evacuation from Disaster Area

Referring to the Nagel–Schreckenberg’s (NaSch) model, we have studied the impact of agent and diligent driver into the micro traffic model in the case of evacuation. This study is attention to the deceleration that added in the micro traffic model. The effect of deceleration to simulation for evacuation from disaster area is considered. The traffic flow property is studied by analyzing the time-space diagram. The simulation results show that deceleration caused the evacuation time increases when we compare it by without deceleration

Buffered Simulation Games for B\"uchi Automata

Simulation relations are an important tool in automata theory because they provide efficiently computable approximations to language inclusion. In recent years, extensions of ordinary simulations have been studied, for instance multi-pebble and multi-letter simulations which yield better approximations and are still polynomial-time computable. In this paper we study the limitations of approximating language inclusion in this way: we introduce a natural extension of multi-letter simulations called buffered simulations. They are based on a simulation game in which the two players share a FIFO buffer of unbounded size. We consider two variants of these buffered games called continuous and look-ahead simulation which differ in how elements can be removed from the FIFO buffer. We show that look-ahead simulation, the simpler one, is already PSPACE-hard, i.e. computationally as hard as language inclusion itself. Continuous simulation is even EXPTIME-hard. We also provide matching upper bounds for solving these games with infinite state spaces.Comment: In Proceedings AFL 2014, arXiv:1405.527