Related papers: First Order Alternation
Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware. The main advantage of the alternating model of computation is that complementation is…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model…
A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages which is closed under boolean operations…
First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…
In this paper we give automata-based representation of LTL-FO$^+$ properties. LTL-FO$^+$ is an extension of LTL that includes first-order quantification over bounded variable, thus greatly increasing the expressivity of the language. An…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
We develop a general framework for the specification and implementation of systems whose executions are words, or partial orders, over an infinite alphabet. As a model of an implementation, we introduce class register automata, a one-way…
We present new results on realtime alternating, private alternating, and quantum alternating automaton models. Firstly, we show that the emptiness problem for alternating one-counter automata on unary alphabets is undecidable. Then, we…
Alternating timed automata (ATA) are an extension of timed automata, that are closed under complementation and hence amenable to logic-to-automata translations. Several timed logics, including Metric Temporal Logic (MTL), can be converted…
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…
We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…
We introduce Symbolic Alternating Finite Automata (s-AFA) as an expressive, succinct, and decidable model for describing sets of finite sequences over arbitrary alphabets. Boolean operations over s-AFAs have linear complexity, which is in…
Several new algorithms for deciding emptiness of Boolean combinations of regular languages and of languages of alternating automata (AFA) have been proposed recently, especially in the context of analysing regular expressions and in string…
These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…
We consider two-variable first-order logic $\text{FO}^2$ and its quantifier alternation hierarchies over both finite and infinite words. Our main results are forbidden patterns for deterministic automata (finite words) and for Carton-Michel…
First-order logic is a natural way of expressing the properties of computation, traditionally used in various program logics for expressing the correctness properties and certificates. Subsequently, modern methods in the automated inference…
We present a knowledge compilation approach for existential and universal quantification in alternating automata. Knowledge compilation transforms formulas into normal forms with special properties that enable efficient answering of…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
Alternating timed automata on infinite words are considered. The main result is a characterization of acceptance conditions for which the emptiness problem for these automata is decidable. This result implies new decidability results for…