TY - JOUR
T1 - Choiceless polynomial time
AU - Blass, Andreas
AU - Gurevich, Yuri
AU - Shelah, Saharon
PY - 1999/10/15
Y1 - 1999/10/15
N2 - Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model whose machines do not distinguish between isomorphic structures and compute exactly PTime properties? This question can be recast as follows: Does there exist a logic that captures polynomial time (without presuming the presence of a linear order)? Earlier, one of us conjectured a negative answer. The problem motivated a quest for stronger and stronger PTime logics. All these logics avoid arbitrary choice. Here we attempt to capture the choiceless fragment of PTime. Our computation model is a version of abstract state machines (formerly called evolving algebras). The idea is to replace arbitrary choice with parallel execution. The resulting logic expresses all properties expressible in any other PTime logic in the literature. A more difficult theorem shows that the logic does not capture all of PTime.
AB - Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model whose machines do not distinguish between isomorphic structures and compute exactly PTime properties? This question can be recast as follows: Does there exist a logic that captures polynomial time (without presuming the presence of a linear order)? Earlier, one of us conjectured a negative answer. The problem motivated a quest for stronger and stronger PTime logics. All these logics avoid arbitrary choice. Here we attempt to capture the choiceless fragment of PTime. Our computation model is a version of abstract state machines (formerly called evolving algebras). The idea is to replace arbitrary choice with parallel execution. The resulting logic expresses all properties expressible in any other PTime logic in the literature. A more difficult theorem shows that the logic does not capture all of PTime.
KW - Abstract state machine
KW - Choice
KW - Parallelism
KW - Polynomial time
KW - Unordered structures
UR - http://www.scopus.com/inward/record.url?scp=0033569294&partnerID=8YFLogxK
U2 - 10.1016/S0168-0072(99)00005-6
DO - 10.1016/S0168-0072(99)00005-6
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AN - SCOPUS:0033569294
SN - 0168-0072
VL - 100
SP - 141
EP - 187
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 1-3
ER -