相关论文: Deciding $k$CFA is complete for EXPTIME
Challenging the standard notion of totality in computable functions, one has that, given any sufficiently expressive formal axiomatic system, there are total functions that, although computable and "intuitively" understood as being total,…
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 study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
Recently, we introduced the notion of flow (depending on time) of finite-dimensional algebras. A flow of algebras (FA) is a particular case of a continuous-time dynamical system whose states are finite-dimensional algebras with (cubic)…
A worst-case ExpTime tableau-based decision procedure is outlined for the satisfiability problem in $\mathcal{ALCQI}$ w.r.t. general axioms.
The finite satisfiability problem for guarded fixpoint logic is decidable and complete for 2ExpTime (resp. ExpTime for formulas of bounded width).
We address the problem of verifying message passing programs, defined as a set of parallel processes communicating through unbounded FIFO buffers. We introduce a bounded analysis that explores a special type of computations, called…
Open questions with respect to the computational complexity of linear CNF formulas in connection with regularity and uniformity are addressed. In particular it is proven that any l-regular monotone CNF formula is XSAT-unsatisfiable if its…
We consider policy gradient methods for stochastic optimal control problem in continuous time. In particular, we analyze the gradient flow for the control, viewed as a continuous time limit of the policy gradient method. We prove the global…
This paper shows that the satisfiability problem for probabilistic CTL (PCTL, for short) is undecidable. By a reduction from $1\frac{1}{2}$-player games with PCTL winning objectives, we establish that the PCTL satisfiability problem is…
This paper is devoted to the complexity of the Boolean satisfiability problem. We consider a version of this problem, where the Boolean formula is specified in the conjunctive normal form. We prove an unexpected result that the…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "history-free" strategies. This model is shown to capture definability in PCF. More precisely,…
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…
We study the implications of model completeness of a theory for the effectiveness of presentations of models of that theory. It is immediate that for a computable model $\mathcal A$ of a computably enumerable, model complete theory, the…
We present and analyze a natural hierarchy of weak theories, develop analysis in them, and show that they are interpretable in bounded quantifier arithmetic $\text{I}\Delta_0$ (and hence in Robinson arithmetic Q). The strongest theories…
LTL synthesis -- the construction of a function to satisfy a logical specification formulated in Linear Temporal Logic -- is a 2EXPTIME-complete problem with relevant applications in controller synthesis and a myriad of artificial…
We will consider exact controllability of the distributed system governed by the wave equation with memory. It will be proved that this mechanical system can be driven to rest in finite time, the absolute value of the distributed control…
An affine model of computation is defined as a subset of iterated immediate-snapshot runs, capturing a wide variety of shared-memory systems, such as wait-freedom, t-resilience, k-concurrency, and fair shared-memory adversaries. The…