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A.: On the complexity of fixedsize bitvector logics with binary encoded bitwidth
 In: Proc. SMT’12
, 2012
"... Bitprecise reasoning is important for many practical applications of Satisfiability Modulo Theories (SMT). In recent years efficient approaches for solving fixedsize bitvector formulas have been developed. From the theoretical point of view, only few results on the complexity of fixedsize bitve ..."
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Cited by 12 (6 self)
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Bitprecise reasoning is important for many practical applications of Satisfiability Modulo Theories (SMT). In recent years efficient approaches for solving fixedsize bitvector formulas have been developed. From the theoretical point of view, only few results on the complexity of fixedsize bitvector logics have been published. In this paper we show that some of these results only hold if unary encoding on the bitwidth of bitvectors is used. We then consider fixedsize bitvector logics with binary encoded bitwidth and establish new complexity results. Our proofs show that binary encoding adds more expressiveness to bitvector logics, e.g. it makes fixedsize bitvector logic even without uninterpreted functions nor quantification NExpTimecomplete. We also show that under certain restrictions the increase of complexity when using binary encoding can be avoided. 1
More on the Complexity of QuantifierFree FixedSize BitVector Logics with Binary Encoding
"... Abstract. Bitprecise reasoning is important for many practical applications of Satisfiability Modulo Theories (SMT). In recent years, efficient approaches for solving fixedsize bitvector formulas have been developed. From the theoretical point of view, only few results on the complexity of fixed ..."
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Cited by 3 (1 self)
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Abstract. Bitprecise reasoning is important for many practical applications of Satisfiability Modulo Theories (SMT). In recent years, efficient approaches for solving fixedsize bitvector formulas have been developed. From the theoretical point of view, only few results on the complexity of fixedsize bitvector logics have been published. Most of these results only hold if unary encoding on the bitwidth of bitvectors is used. In previous work [1], we showed that binary encoding adds more expressiveness to bitvector logics, e.g. it makes fixedsize bitvector logic without uninterpreted functions nor quantification NExpTimecomplete. In this paper, we look at the quantifierfree case again and propose two new results. While it is enough to consider logics with bitwise operations, equality, and shift by constant to derive NExpTimecompleteness, we show that the logic becomes PSpacecomplete if, instead of shift by constant, only shift by 1 is permitted, and even NPcomplete if no shifts are allowed at all. 1
Decision Procedure for an Extension of WS1S
, 2001
"... We define an extension of the weak monadic secondorder logic of one successor (WS1S) with an infinite family of relations and show its decidability. Analogously to the decision procedure for WS1S, automata are used. But instead of using word automata, we use tree automata that accept or reject word ..."
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We define an extension of the weak monadic secondorder logic of one successor (WS1S) with an infinite family of relations and show its decidability. Analogously to the decision procedure for WS1S, automata are used. But instead of using word automata, we use tree automata that accept or reject words. In particular, we encode a word in a complete leaf labeled tree and restrict the acceptance condition for tree automata to trees that encode words. As applications, we show how this extension can be applied to reason automatically about parameterized families of combinational treestructured circuits and used to solve certain decision problems.