We propose a query learning algorithm for residual symbolic finite automata (RSFAs). Symbolic finite automata (SFAs) are finite automata whose transitions are labeled by predicates over a Boolean algebra, in which a big collection of characters leading the same transition may be represented by a single predicate. Residual finite automata (RFAs) are a special type of non-deterministic finite automata which can be exponentially smaller than the minimum deterministic finite automata and have a favorable property for learning algorithms. RSFAs have both properties of SFAs and RFAs and can have more succinct representation of transitions and fewer states than RFAs and deterministic SFAs accepting the same language. The implementation of our algorithm efficiently learns RSFAs over a huge alphabet and outperforms an existing learning algorithm for deterministic SFAs. The result also shows that the benefit of non-determinism in efficiency is even larger in learning SFAs than non-symbolic automata.
Ben-Gurion University（本-古里安大学）；The Technion（以色列理工学院）；University of Regina（里贾纳大学）
We revisit the complexity of procedures on SFAs (such as intersection, emptiness, etc.) and analyze them according to the measures we find suitable for symbolic automata: the number of states, the maximal number of transitions exiting a state, and the size of the most complex transition predicate. We pay attention to the special forms of SFAs: {normalized SFAs} and {neat SFAs}, as well as to SFAs over a {monotonic} effective Boolean algebra.
Symbolic Finite Automata and Register Automata are two orthogonal extensions of finite automata motivated by real-world problems where data may have unbounded domains. These automata address a demand for a model over large or infinite alphabets, respectively. Both automata models have interesting applications and have been successful in their own right. In this paper, we introduce Symbolic Register Automata, a new model that combines features from both symbolic and register automata, with a view on applications that were previously out of reach. We study their properties and provide algorithms…
We propose an automaton model which is a combination of symbolic and register automata, i.e., we enrich symbolic automata with memory. We call such automata Register Match Automata (RMA). RMA extend the expressive power of symbolic automata, by allowing formulas to be applied not only to the last element read from the input string, but to multiple elements, stored in their registers. RMA also extend register automata, by allowing arbitrary formulas, besides equality predicates. We study the closure properties of RMA under union, concatenation, Kleene+, complement and determinization and show t…
National and Kapodistrian University of Athens（雅典国立与卡波季斯特里亚大学）；National Center for Scientific Research “Demokritos”（德谟克利特国家科学研究中心）；University of Piraeus（比雷埃夫斯大学）
We propose an automaton model which is a combination of symbolic and register automata, i.e., we enrich symbolic automata with memory. We call such automata Symbolic Register Automata (SRA). SRA extend the expressive power of symbolic automata, by allowing Boolean formulas to be applied not only to the last element read from the input string, but to multiple elements, stored in their registers. SRA also extend register automata, by allowing arbitrary Boolean formulas, besides equality predicates. We study the closure properties of SRA under union, intersection, concatenation, Kleene closure, c…
We investigate means of efficient computation of the simulation relation over symbolic finite automata (SFAs), i.e., finite automata with transitions labeled by predicates over alphabet symbols. In one approach, we build on the algorithm by Ilie, Navaro, and Yu proposed originally for classical finite automata, modifying it using the so-called mintermisation of the transition predicates. This solution, however, generates all Boolean combinations of the predicates, which easily causes an exponential blowup in the number of transitions. Therefore, we propose two more advanced solutions. The firs…
We propose a new symbolic trace semantics for register automata (extended finite state machines) which records both the sequence of input symbols that occur during a run as well as the constraints on input parameters that are imposed by this run. Our main result is a generalization of the classical Myhill-Nerode theorem to this symbolic setting. Our generalization requires the use of three relations to capture the additional structure of register automata. Location equivalence $\equiv_l$ captures that symbolic traces end in the same location, transition equivalence $\equiv_t$ captures that the…
Given a specification of linear-time temporal logic interpreted over finite traces (LTLf), the reactive synthesis problem asks to find a finitely-representable, terminating controller that reacts to the uncontrollable actions of an environment in order to enforce a desired system specification. In this paper we study, for the first time, the reactive synthesis problem for DECLARE - a fragment of LTLf extensively used both in theory and practice for specifying declarative, constraint-based business processes. We provide a threefold contribution. First, we give a naive, doubly exponential time s…
Translating formulas of Linear Temporal Logic (LTL) over finite traces, or LTLf, to symbolic Deterministic Finite Automata (DFA) plays an important role not only in LTLf synthesis, but also in synthesis for Safety LTL formulas. The translation is enabled by using MONA, a powerful tool for symbolic, BDD-based, DFA construction from logic specifications. Recent works used a first-order encoding of LTLf formulas to translate LTLf to First Order Logic (FOL), which is then fed to MONA to get the symbolic DFA. This encoding was shown to perform well, but other encodings have not been studied. Specif…
A modular architecture for transparent computation in Recurrent Neural Networks
Plymouth University（普利茅斯大学）；Bernstein Center for Computational Neuroscience Berlin（柏林伯恩斯坦计算神经科学中心）；Humboldt-Universität zu Berlin（柏林洪堡大学）；Inria Sophia-Antipolis Méditerranée（法国国家信息与自动化研究所索菲亚-安蒂波利斯地中海研究中心）
Temporal logic is often used to describe temporal properties in AI applications. The most popular language for doing so is Linear Temporal Logic (LTL). Recently, LTL on finite traces, LTLf, has been investigated in several contexts. In order to reason about LTLf, formulas are typically compiled into deterministic finite automata (DFA), as the intermediate semantic representation. Moreover, due to the fact that DFAs have canonical representation, efficient minimization algorithms can be applied to maximally reduce DFA size, helping to speed up subsequent computations. Here, we present a thoroug…
University of the Basque Country（巴斯克大学）；foldAI；Bernstein Center for Computational Neuroscience（伯恩斯坦计算神经科学中心）；Basque Center for Applied Mathematics（巴斯克应用数学中心）
Computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. A particular way for combining these approaches within a framework called vector symbolic architectures leads to neural automata. An interesting research direction we have pursued under this framework has been to consider mapping symbolic dynamics onto neurodynamics, represented as neural automata. This representation theory, enables us to ask questions, such as, how does the brain implement Turing computations. Specifically, in this representation theory, neural automata result from the assig…
Complex Event Recognition with Symbolic Register Transducers: Extended Technical Report
Institute of Informatics & Telecommunications, National Center for Scientific Research “Demokritos”（希腊德谟克利特国家科学研究中心信息学与电信研究所）；Department of Maritime Studies, University of Piraeus（比雷埃夫斯大学海事研究系）
We present abstraction-refinement algorithms for model checking safety properties of timed automata. The abstraction domain we consider abstracts away zones by restricting the set of clock constraints that can be used to define them, while the refinement procedure computes the set of constraints that must be taken into consideration in the abstraction so as to exclude a given spurious counterexample. We implement this idea in two ways: an enumerative algorithm where a lazy abstraction approach is adopted, meaning that possibly different abstract domains are assigned to each exploration node; a…
We present an algorithm for active learning of deterministic timed automata with a single clock. The algorithm is within the framework of Angluin's $L^*$ algorithm and inspired by existing work on the active learning of symbolic automata. Due to the need of guessing for each transition whether it resets the clock, the algorithm is of exponential complexity in the size of the learned automata. Before presenting this algorithm, we propose a simpler version where the teacher is assumed to be smart in the sense of being able to provide the reset information. We show that this simpler setting yield…
We present $L^{\#}$, a new and simple approach to active automata learning. Instead of focusing on equivalence of observations, like the $L^{\ast}$ algorithm and its descendants, $L^{\#}$ takes a different perspective: it tries to establish apartness, a constructive form of inequality. $L^{\#}$ does not require auxiliary notions such as observation tables or discrimination trees, but operates directly on tree-shaped automata. $L^{\#}$ has the same asymptotic query and symbol complexities as the best existing learning algorithms, but we show that adaptive distinguishing sequences can be natural…
We propose an algorithm for schema-based determinization of finite automata on words and of step-wise hedge automata on nested words. The idea is to integrate schema-based cleaning directly into automata determinization. We prove the correctness of our new algorithm and show that it is alway smore efficient than standard determinization followed by schema-based cleaning. Our implementation permits to obtain a small deterministic automaton for an example of an XPath query, where standard determinization yields a huge stepwise hedge automaton for which schema-based cleaning runs out of memory.
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for computations. Quantum automata can be classified thusly: quantum finite automata, quantum sequential machine, quantum pushdown automata, quantum Turing machine and orthomodular lattice-valued automata. These models are useful for determining the expressive power and boundaries of various computational features. In light of the current state of quantum computation …
Monitoring of a signal plays an essential role in the runtime verification of cyber-physical systems. Qualitative timed pattern matching is one of the mathematical formulations of monitoring, which gives a Boolean verdict for each sub-signal according to the satisfaction of the given specification. There are two orthogonal directions of extension of the qualitative timed pattern matching. One direction on the result is quantitative: what engineers want is often not a qualitative verdict but the quantitative measurement of the satisfaction of the specification. The other direction on the algori…
Deterministic finite automata are one of the simplest and most practical models of computation studied in automata theory. Their conceptual extension is the non-deterministic finite automata which also have plenty of applications. In this article, we study these models through the lens of succinct data structures where our ultimate goal is to encode these mathematical objects using information-theoretically optimal number of bits along with supporting queries on them efficiently. Towards this goal, we first design a succinct data structure for representing any deterministic finite automaton $\…
We introduce an automata model for describing interesting classes of differential privacy mechanisms/algorithms that include known mechanisms from the literature. These automata can model algorithms whose inputs can be an unbounded sequence of real-valued query answers. We consider the problem of checking whether there exists a constant $d$ such that the algorithm described by these automata are $dε$-differentially private for all positive values of the privacy budget parameter $ε$. We show that this problem can be decided in time linear in the automaton's size by identifying a necessary and s…
