Complementing deterministic Büchi automata in polynomial time

AbstractFor any Buchi automaton Γ with n states which accepts the (ω-regular) language L(Γ), an explicit construction is given for a Büchi automaton Γ with 2n states which, when Γ is deterministic, accepts exactly the complementary language L(Γ)′. It follows that the nonemptiness of complement problem for deterministic Buchi automata (i.e., whether L(Γ)′ = ⊘) is solvable in polynomial time. The best previously known construction for complementing a deterministic Büchi automaton with n states has O(24n2) states; for nondeterministic Γ, determining whether L(Γ)′ = ⊘, is known to be PSPACE-complete. Interest in deterministic Büchi automata arises from the suitability of deterministic automata in general to describe properties of physical systems; such properties have been found to be more naturally expressible by deterministic automata than by nondeterministic automata. However, if Γ is nondeterministic, then Γ provides a “poor man's” approximate inverse to Γ in the following sense: L(Γ)′ ⊂ L(Γ), and as nondeterministic branches of T are removed, the two languages become closer. Hence, for example, given two nondeterministic Buchi automata Λ and Γ, one may test for containment of their associated languages through use of the corollary that L (Λ ∗ Γ = ⊘ ⇒ L (Λ) ⊂ L(Γ) (where Γ ∗ Γ is one of the standard constructions satisfying L (Λ ∗ Γ) = L (Λ) ∩ L(Γ)). The “error term” L = L(Γ) ⧹ L(Γ)′ may be deter exactly, and whether L = ⊘ may be determined in time O(e2), where e is the number of edges of Γ

Systematic AI Approach for AGI: Addressing Alignment, Energy, and AGI Grand Challenges

AI faces a trifecta of grand challenges the Energy Wall, the Alignment Problem and the Leap from Narrow AI to AGI. Contemporary AI solutions consume unsustainable amounts of energy during model training and daily operations.Making things worse, the amount of computation required to train each new AI model has been doubling every 2 months since 2020, directly translating to increases in energy consumption.The leap from AI to AGI requires multiple functional subsystems operating in a balanced manner, which requires a system architecture. However, the current approach to artificial intelligence lacks system design; even though system characteristics play a key role in the human brain from the way it processes information to how it makes decisions. Similarly, current alignment and AI ethics approaches largely ignore system design, yet studies show that the brains system architecture plays a critical role in healthy moral decisions.In this paper, we argue that system design is critically important in overcoming all three grand challenges. We posit that system design is the missing piece in overcoming the grand challenges.We present a Systematic AI Approach for AGI that utilizes system design principles for AGI, while providing ways to overcome the energy wall and the alignment challenges.Comment: International Journal on Semantic Computing (2024) Categories: Artificial Intelligence; AI; Artificial General Intelligence; AGI; System Design; System Architectur

An automatic abstraction technique for verifying featured, parameterised systems

A general technique combining model checking and abstraction is presented that allows property based analysis of systems consisting of an arbitrary number of featured components. We show how parameterised systems can be specified in a guarded command form with constraints placed on variables which occur in guards. We prove that results that hold for a small number of components can be shown to scale up. We then show how featured systems can be specified in a similar way, by relaxing constraints on guards. The main result is a generalisation theorem for featured systems which we apply to two well known examples

Membership Questions for Timed and Hybrid Automata

Timed and hybrid automata are extensions of finite-state machines for formal modeling of embedded systems with both discrete and continuous components. Reachability problems for these automata are well studied and have been implemented in verification tools. In this paper, for the purpose of effective error reporting and testing, we consider the membership problems for such automata. We consider different types of membership problems depending on whether the path (i.e. edge-sequence), or the trace (i.e. event-sequence), or the timed trace (i.e. timestamped event-sequence), is specified. We give comprehensive results regarding the complexity of these membership questions for different types of automata, such as timed automata and linear hybrid automata, with and without ε-transitions. In particular, we give an efficient O (n.m2) algorithm for generating timestamps corresponding a path of length n in a timed automaton with m clocks. This algorithm is implemented in the verifier COSPAN to improve its diagnostic feedback during timing verification. Second, we show that for automata without ε-transitions, the membership question is NP-complete for different types of automata whether or not the timestamps are specified along with the trace. Third, we show that for automata with ε-transitions, the membership question is as hard as the reachability question even for timed traces: it is PSPACE-complete for timed automata, and undecidable for slight generalizations

The Neural Basis of the Number Sense

<p>The ability to enumerate approximately without counting is an evolutionarily ancient and developmentally early core cognitive ability known as the "number sense". We use the number sense when we estimate a number without counting individual items, as when we guess the number of people in a crowded room. The number sense is theorized to form an instinctual building block upon which we create the conceptual structures of mathematics. This dissertation addresses three research questions regarding the number sense. </p><p> The first is the question of whether the number sense is malleable, and if so, what are the neural correlates of malleability. In Chapter 2 we gave adults number sense training, which we found improved the accuracy of numerical estimation. In Chapter 4 we recorded from single neurons in monkeys while they viewed arrays of items on a computer screen. Similar recordings have been made previously, but usually using monkeys that were trained to discriminate sets based on number. Recordings in trained animals demonstrated that individual neurons in the monkey's brain track the number of items in a set. We reasoned that if the neural correlates of the number sense were altered by the training experience, then we would get different results in untrained monkeys. We did find neurons encoding numerical information in untrained monkeys, but at lower rates than described previously. Thus, we demonstrated that the number sense can improve with experience, and our data suggest that changes in the proportion of neurons encoding number may subserve this improvement.</p><p> The second question is how to resolve the problem of stimulus control in laboratory tests of the number sense. Typically, number sense function is assessed by presenting arrays of dots on a computer screen. In such stimuli, however, non-numerical features necessarily covary with numerical features. By counter-balancing different stimulus conditions, it is possible to determine if number and not some other feature is influencing a dependent measure. In Chapter 3, we develop a technique to go further and determine which of eleven stimulus features is influencing a dependent measure. </p><p> The third question is whether the intraparietal sulcus (IPS), a brain area known to be engaged during numerical cognition, is specialized for it. To address this question, we apply the technique developed in Chapter 3 to the neural data recorded from monkeys in Chapter 4. We show that the IPS does contain number neurons; however, it also contains neurons that encode many other features in equal proportion, indicating that it is not specialized for number. In Chapter 5, we use drugs injected into the IPS to reversibly inactivate it. We found that after IPS inactivation, performance on a numerical discrimination task was impaired but no more so than a color discrimination control task. Again, our data do not support the theory that the IPS is specialized for numerical processing.</p>Dissertatio

A model checking-based approach for security policy verification of mobile systems

International audienceThis article describes an approach for the automated verification of mobile systems. Mobile systems are characterized by the explicit notion of (e.g., sites where they run) and the ability to execute at different locations, yielding a number of security issues. To this aim, we formalize mobile systems as Labeled Kripke Structures, encapsulating the notion of that describes the hierarchical nesting of the threads constituting the system. Then, we formalize a generic that includes rules for expressing and manipulating the code location. In contrast to many other approaches, our technique supports both access control and information flow specification. We developed a prototype framework for model checking of mobile systems. It works directly on the program code (in contrast to most traditional process-algebraic approaches that can model only limited details of mobile systems) and uses abstraction-refinement techniques, based also on location abstractions, to manage the program state space. We experimented with a number of mobile code benchmarks by verifying various security policies. The experimental results demonstrate the validity of the proposed mobile system modeling and policy specification formalisms and highlight the advantages of the model checking-based approach, which combines the validation of security properties with other checks, such as the validation of buffer overflows