Memory system and information processing system

An information processing system comprising:

• a host;
• and
• a memory system capable of being connected to the host,
• wherein the memory system comprises a non-volatile memory,
• the host is configured to manage a data map for managing validity of data written in the non-volatile memory,
• the data map has a hierarchical structure including at least a first hierarchy and a second hierarchy higher than the first hierarchy, and comprises a plurality of first fragment tables corresponding to the first hierarchy and a second fragment table corresponding to the second hierarchy,
• each of the first fragment tables has a predetermined number of entries, each of the entries having information indicating the validity of each data having a predetermined size written in a first range of physical address in the non-volatile memory,
• the second fragment table is used to manage reference destination information for referencing each of the first fragment tables,
• the host is configured to update the data map when receiving a command for invalidating data written in the non-volatile memory,
• the reference destination information has a plurality of address information, each of the plurality of address information is an address where each of the first fragment tables is stored, and
• when all of the plurality of data written in the first range of physical address allocated to the first fragment table is invalidated, invalidity is set in an entry of the second fragment table allocated the first range of physical address.