Related papers: The Complexity of Flat Freeze LTL

We introduce the class of tree constraint automata with data values in Z (equipped with the less than relation and equality predicates to constants) and we show that the nonemptiness problem is ExpTime-complete. Using an automata-based…

We prove that some fairly basic questions on automata reading infinite words depend on the models of the axiomatic system ZFC. It is known that there are only three possibilities for the cardinality of the complement of an omega-language…

Synthesis of models and strategies is a very important problem in software engineering. The main element here is checking the satisfiability of formulae expressing the specification of a system to be implemented. This paper puts forward a…

Algorithms for model checking and satisfiability of the modal $\mu$-calculus start by converting formulas to alternating parity tree automata. Thus, model checking is reduced to checking acceptance by tree automata and satisfiability to…

In this paper we study the family of freezing cellular automata (FCA) in the context of asynchronous updating schemes. A cellular automaton is called freezing if there exists an order of its states, and the transitions are only allowed to…

Automata over infinite alphabets have recently come to be studied extensively as potentially useful tools for solving problems in verification and database theory. One popular model of automata studied is the Class Memory Automata (CMA),…

We classify the complexity of the LTL satisfiability and model checking problems for several standard parameterisations. The investigated parameters are temporal depth, number of propositional variables and formula treewidth, resp.,…

We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear Dynamic Logic (LDL) by temporal operators equipped with parameters that bound their scope. LDL itself was proposed as an extension of Linear Temporal Logic (LTL) that…

Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…

Timed automata (TAs) are an extension of finite automata that can measure and react to the passage of time, providing the ability to handle real-time constraints using clocks. In 2009, Franck Cassez showed that the timed opacity problem,…

We determine the complexity of second-order HyperLTL satisfiability, finite-state satisfiability, and model-checking: All three are equivalent to truth in third-order arithmetic. We also consider two fragments of second-order HyperLTL that…

We study the reachability problem for one-counter automata in which transitions can carry disequality tests. A disequality test is a guard that prohibits a specified counter value. This reachability problem has been known to be NP-hard and…

This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…

Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these…

In runtime verification, monitoring consists of analyzing the current execution of a system and determining, on the basis of the observed finite trace, whether all its possible continuations satisfy or violate a given specification. This is…

In this note, we provide complexity characterizations of model checking multi-pushdown systems. Multi-pushdown systems model recursive concurrent programs in which any sequential process has a finite control. We consider three standard…

Continuing the study of complexity theory of Koepke's Ordinal Turing Machines (OTMs) that was started by Rin, L\"owe and the author, we prove the following results: (1) An analogue of Ladner's theorem for OTMs holds: That is, there are…

While model checking PCTL for Markov chains is decidable in polynomial-time, the decidability of PCTL satisfiability, as well as its finite model property, are long standing open problems. While general satisfiability is an intriguing…

Module checking has been introduced in late 1990s to verify open systems, i.e., systems whose behavior depends on the continuous interaction with the environment. Classically, module checking has been investigated with respect to…

Priced timed automata provide a natural model for quantitative analysis of real-time systems and have been successfully applied in various scheduling and planning problems. The optimal reachability problem for linearly-priced timed automata…