Related papers: HyperLTL Satisfiability Is Highly Undecidable, Hyp…
We study the realizability problem for Safety LTL, the syntactic fragment of Linear Temporal Logic capturing safe formulas. We show that the problem is EXP-complete, disproving the existing conjecture of 2EXP-completeness. We achieve this…
Computation Tree Logic (CTL) and its extensions CTL* and CTL+ are widely used in automated verification as a basis for common model checking tools. But while they can express many properties of interest like reachability, even simple…
Adding propositional quantification to the modal logics K, T or S4 is known to lead to undecidability but CTL with propositional quantification under the tree semantics (tQCTL) admits a non-elementary Tower-complete satisfiability problem.…
This paper proposes a new logic RoCTL* to model robustness in concurrent systems. RoCTL* extends CTL* with the addition of Obligatory and Robustly operators, which quantify over failure-free paths and paths with one more failure…
In this paper, we propose a new logic for expressing and reasoning about probabilistic hyperproperties. Hyperproperties characterize the relation between different independent executions of a system. Probabilistic hyperproperties express…
We show that the finite satisfiability problem for the unary negation fragment with arbitrary number of transitive relations is decidable and 2-ExpTime-complete. Our result actually holds for a more general setting in which one can require…
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…
We study succinctness as a measure of the expressive power of transformers. Succinctness -- how compactly a formalism can describe a language relative to other formalisms -- is a classical notion in logic and automata theory. We prove that…
Uniform one-dimensional fragment UF1^= is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified…
Linear-time temporal logic on finite traces (LTLf) is rapidly becoming a de-facto standard to produce specifications in many application domains (e.g., planning, business process management, run-time monitoring, reactive synthesis). Several…
Linear temporal logic (LTL) has recently been adopted as a powerful formalism for specifying complex, temporally extended tasks in multi-task reinforcement learning (RL). However, learning policies that efficiently satisfy arbitrary…
We analyse the complexity of the satisfiability problem ssmSAT for State Space Models (SSM), which asks whether an input sequence can lead the model to an accepting configuration. We find that ssmSAT is undecidable in general, reflecting…
Linear Temporal Logic (LTL) is widely used for defining conditions on the execution paths of dynamic systems. In the case of dynamic systems that allow for nondeterministic evolutions, one has to specify, along with an LTL formula f, which…
Ensuring large language model (LLM) reliability requires distinguishing objective unsolvability (inherent contradictions) from subjective capability limitations (tasks exceeding model competence). Current LLMs often conflate these…
Hyperproperties are properties that refer to multiple computation traces. This includes many information-flow security policies, such as observational determinism, (generalized) noninterference, and noninference, and other system properties…
Interval temporal logics provide a general framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as the primitive ontological entities. In this paper, we identify all fragments…
We investigate the complexity of the satisfiability problem for a modal logic expressing `knowing how' assertions, related to an agent's abilities to achieve a certain goal. We take one of the most standard semantics for this kind of logics…
We propose a formal proof of the undecidability of the model checking problem for alternating- time temporal logic under imperfect information and perfect recall semantics. This problem was announced to be undecidable according to a…
The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…