Under Niyazov, who ruled Turkmenistan for nearly two decades, internet access was tightly restricted to senior state employees and officially approved organisations, embassies and international organisations.
The former president also last year stripped more than 100,000 elderly Turkmens of their pensions, under a law that also cancelled sick leave and maternity leave payments.
Niyazov ruled for 21 years without competing in an election, allowing no open political debate and driving opposition leaders abroad.
He died on December 21 of heart failure.
A likely winner
"I want to be president of a democratic country, where rich people live and work, where all conditions for free life and free work are created"
Gurbanguli Berdymukhamedov Acting president of Turkmenistan
However, hopes of radical political change have been tempered by Berdymukhamedov's promises to "steadfastly follow the bidding of the great Saparmurat Turkmenbashi," using the title meaning 'Father of All Turkmen' that Niyazov bestowed on himself.
Berdymukhamedov is one of six candidates for the February 11 presidential election.
All candidates were chosen by the country's highest legislative body and Turkmenistan has only one legal political party - the Democratic Party of Turkmenistan - a descendent of the country's former communist party.
Berdymukhamedov is expected to win by a comfortable margin.
Berdymukhamedov told voters that that he would liberalise the country's poorly-performing economy.
"One of the main tasks is to give the population work, to develop small and medium business," he said.
"Sixty one per cent of our economy is in private hands and I will support businessmen."
Berdymukhamedov also promised voters that the elections will be "just, honest and open," the state media reports said.
"I want to be president of a democratic country, where rich people live and work, where all conditions for free life and free work are created," he was quoted as saying.