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We connect the study of pseudodeterministic algorithms to two major open problems about the structural complexity of $\mathsf{BPTIME}$: proving hierarchy theorems and showing the existence of complete problems. Our main contributions can be…
Model-checking the alternating-time temporal logics ATL and ATL* with incomplete information is undecidable for perfect recall semantics. However, when restricting to memoryless strategies the model-checking problem becomes decidable. In…
The effects of gain and loss on the band structures of a bulk topological dielectric photonic crystal (PC) with $C_{6v}$ symmetry and the PC-air-PC interface are studied based on first-principle calculation. To illustrate the importance of…
The coherent population trapping (CPT) effect is used for making compact atomic clocks. There are two types of CPT clocks: the one in which the Raman beams are applied continuously and the one in which two CPT pulses separated by a dark…
We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the…
This paper considers the state estimation problem for nonlinear dynamic systems with unknown but bounded noises. Set membership filter (SMF) is a popular algorithm to solve this problem. In the set membership setting, we investigate the…
This work establishes a rigorous theoretical foundation for analyzing deep learning systems by leveraging Infinite Time Turing Machines (ITTMs), which extend classical computation into transfinite ordinal steps. Using ITTMs, we reinterpret…
The deployment of autonomous systems in safety-critical environments requires control policies that guarantee satisfaction of complex control specifications. These systems are commonly modeled as nonlinear discrete-time stochastic systems.…
In this technical note, a recursive set-membership filtering algorithm for discrete-time nonlinear dynamical systems subject to unknown but bounded process and measurement noises is proposed. The nonlinear dynamics is represented in a…
We extend the $CPT$ theorem to quantum field theories with non-Hermitian Hamiltonians and unstable states. Our derivation is a quite minimal one as it requires only the time independent evolution of scalar products, invariance under complex…
Parametric timed automata extend the standard timed automata with the possibility to use parameters in the clock guards. In general, if the parameters are real-valued, the problem of language emptiness of such automata is undecidable even…
This paper considers the question of P = NP in context of the polynomial time SAT algorithm. It posits proposition dependent on existence of conjectured problem that even where the algorithm is shown to solve SAT in polynomial time it…
In (Kabanets, Impagliazzo, 2004) it is shown how to decide the circuit polynomial identity testing problem (CPIT) in deterministic subexponential time, assuming hardness of some explicit multilinear polynomial family for arithmetical…
The verification of systems combining hard timing constraints with concurrency is challenging. This challenge becomes even harder when some timing constants are missing or unknown. Parametric timed formalisms, such as parametric timed…
We consider the totally asymmetric exclusion process in discrete time with generalized updating rules. We introduce a control parameter into the interaction between particles. Two particular values of the parameter correspond to known…
We show that for continuous time dynamical systems described by polynomial differential equations of modest degree (typically equal to three), the following decision problems which arise in numerous areas of systems and control theory…
Interrupt Timed Automata (ITA) is an expressive timed model, introduced to take into account interruptions, according to levels. Due to this feature, this formalism is incomparable with Timed Automata. However several decidability results…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes…
Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm…