A disease characterized by progressive dementia and periodic sharp wave complexes on the EEG is:

Creutzfeldt-Jakob disease (CJD) is characterized by rapidly progressing dementia and is often associated with distinctive periodic sharp wave complexes on the electroencephalogram (EEG). This prion disease leads to a severe neurological decline, and the EEG findings are a hallmark of the condition. The periodic sharp wave complexes reflect the underlying neurodegenerative processes occurring in the brain, which contributes to the cognitive deficits seen in patients.

In this context, the other diseases mentioned do not specifically align with both the progressive dementia and the presence of periodic sharp wave complexes. For instance, Wilson's disease primarily involves hepatic dysfunction and movement disorders due to copper accumulation and does not prominently feature the same EEG changes. Rasmussen's encephalitis is characterized by unilateral inflammation of the brain leading to seizures and loss of function on one side. Tay-Sachs disease is a genetic disorder that affects nerve cells but predominantly results in profound neurological deterioration without the specific EEG findings associated with CJD.

Therefore, the association of progressive dementia with periodic sharp wave complexes strongly indicates Creutzfeldt-Jakob disease as the correct answer.