German public questions refugee policy

While none of the attacks are related, at least two of the four appear to have been carried out by asylum seekers.

Sunday's bombing, which killed only the attacker himself but injured 12 others, was carried out by a 27-year-old Syrian national in the southern city of Ansbach. The attacker's application for asylum had been rejected a year earlier but he was able to stay in the country.

Just hours before, another 21-year-old Syrian asylum seeker killed a woman in a separate machete attack in Reutlingen.

The country was already reeling from a shooting spree in Munich on Friday by an 18-year-old German-Iranian that left nine people dead. That attacker was not an asylum seeker -- he was born and raised in Munich.

And last Monday, a 17-year-old carried out an ax attack on board a train outside of Wurzburg. He was originally reported to be an Afghan refugee, but his nationality and refugee status have since come into question.

As Germany grapples with an extraordinary week of violence, critics have raised concerns over the system for admitting and settling asylum seekers and migrants from war-ravaged countries.

Here are some questions answered about how the system works:

Who can stay?

Sunday's suicide bomber entered Germany two years ago and his application for asylum had been rejected, according to authorities.

But he was able to remain in the country as rejected applicants cannot legally be deported to a place where they face serious harm -- Syria's war zone is clearly one of them.

This leaves the bomber, and many more asylum seekers like him, in a state of limbo, both unable to gain residential status or return to their homeland.

"While they wait for an appeal to go through or a change in their circumstances, they're also not permitted to work or receive benefits," explained CNN's Tim Lister, who estimated that tens of thousands of migrants in Germany were in this position.

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