Efficient modeling of memory arrays in symbolic ternary simulation

Abstract

Abstract. This paper enables symbolic ternary simulation of systems with large embedded memories. Each memory array is replaced with a behavioral model, where the number of symbolic variables used to characterize the initial state of the memory is proportional to the number of distinct symbolic memory locations accessed. The behavioral model provides a conservative approximation of the replaced memory array, while allowing the address and control inputs of the memory to accept symbolic ternary values. Memory state is represented by a list of entries encoding the sequence of updates of symbolic addresses with symbolic data. The list interacts with the rest of the circuit by means of a software interface developed as part of the symbolic simulation engine. This memory model was incorporated into our verification tool based on Symbolic Trajectory Evaluation. Experimental results show that the new model significantly outperforms the transistor level memory model when verifying a simple pipelined data path.

Verification of pipelined microprocessors by correspondence checking in symbolic ternary simulation

“…This ensures that the Boolean expressions for hard_match and soft_match will not be true simultaneously. For an implementation of the Read operation that yields more precise results, and for a way to optimize the Write operation, the reader is referred to [19].…”

“…A ternary version of the EMM is presented in [19], where the memory address and control inputs are allowed to accept symbolic ternary values, while the EMM will behave as a conservative approximation to the replaced memory array. Conservative approximation means that false positive verification results are guaranteed not to occur, although false negative verification results are possible.…”

“…The contributions of this paper are: 1) combining the memory shadowing technique [5] with the ternary EMM [19] in order to support the efficient symbolic ternary simulation when extending Burch and Dill's pipeline verification method [6] to completely model the functionality of the data path at the bit level; 2) a modified correctness criterion in the form of a commutative diagram targeted to symbolic ternary simulation; 3) a variable-group indexing technique for generating the initial state of EMMs; and 4) experimental results with a shortened MIPS pipeline showing the potential of the new ideas.…”

TLSim and EVC: a term-level symbolic simulator and an efficient decision procedure for the logic of equality with uninterpreted functions and memories

“…Nested ITEs were first used to eliminate uninterpreted functions and uninterpreted predicates in Velev and Bryant (1998c), where bit-level functional units were abstracted with read-only instances of an Efficient Memory Model (Velev and Bryant, 1998a;Velev and Bryant, 1998b)-developed for use in symbolic simulation as a behavioural abstraction of memories, and later adopted in verification tools by Innologic Systems (Hasteer, 1999), and Synopsys (Kölbl et al, 2002).…”

Incorporating timing constraints in the efficient memory model for symbolic ternary simulation

“…It is based on the observation that a single execution sequence typically accesses only a limited number of distinct symbolic locations. While the EMM presented in [13] assumes simulation over symbolic binary values, our later work [14] allows the EMM to accept symbolic ternary values at its address and control inputs, while providing a conservative approximation of the replaced memory array. Conservative approximation means that false positive verification results are guaranteed not to occur, although false negative verification 2 results are possible.…”